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Theorem cnfcom3c 7663
 Description: Wrap the construction of cnfcom3 7661 into an existence quantifier. For any , there is a bijection from to some power of . Furthermore, this bijection is canonical , which means that we can find a single function which will give such bijections for every less than some arbitrarily large bound . (Contributed by Mario Carneiro, 30-May-2015.)
Assertion
Ref Expression
cnfcom3c
Distinct variable group:   ,,,

Proof of Theorem cnfcom3c
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eqid 2436 . 2 CNF CNF
2 eqid 2436 . 2 CNF CNF
3 eqid 2436 . 2 OrdIso CNF OrdIso CNF
4 eqid 2436 . 2 seq𝜔 OrdIso CNF CNF OrdIso CNF seq𝜔 OrdIso CNF CNF OrdIso CNF
5 eqid 2436 . 2 seq𝜔 OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF seq𝜔 OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF
6 eqid 2436 . 2 OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF
7 eqid 2436 . 2 OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF
8 eqid 2436 . 2 OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF
9 eqid 2436 . 2 CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF
10 eqid 2436 . 2 CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF
11 eqid 2436 . 2 CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF seq𝜔 OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF seq𝜔 OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF
12 eqid 2436 . 2 CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF seq𝜔 OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF OrdIso CNF seq𝜔 OrdIso CNF CNF OrdIso CNF OrdIso CNF CNF OrdIso CNF OrdIso CNF
131, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12cnfcom3clem 7662 1
 Colors of variables: wff set class Syntax hints:   wi 4  wex 1550   wcel 1725  wral 2705  wrex 2706  cvv 2956   cdif 3317   cun 3318   wss 3320  c0 3628  cuni 4015   cmpt 4266   cep 4492  con0 4581  com 4845  ccnv 4877   cdm 4878  cima 4881   ccom 4882  wf1o 5453  cfv 5454  (class class class)co 6081   cmpt2 6083  seq𝜔cseqom 6704  c1o 6717   coa 6721   comu 6722   coe 6723  OrdIsocoi 7478   CNF ccnf 7616 This theorem is referenced by:  infxpenc2  7903 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-rep 4320  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701  ax-inf2 7596 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-reu 2712  df-rmo 2713  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-pss 3336  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-tp 3822  df-op 3823  df-uni 4016  df-int 4051  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-tr 4303  df-eprel 4494  df-id 4498  df-po 4503  df-so 4504  df-fr 4541  df-se 4542  df-we 4543  df-ord 4584  df-on 4585  df-lim 4586  df-suc 4587  df-om 4846  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461  df-fv 5462  df-isom 5463  df-ov 6084  df-oprab 6085  df-mpt2 6086  df-1st 6349  df-2nd 6350  df-riota 6549  df-recs 6633  df-rdg 6668  df-seqom 6705  df-1o 6724  df-2o 6725  df-oadd 6728  df-omul 6729  df-oexp 6730  df-er 6905  df-map 7020  df-en 7110  df-dom 7111  df-sdom 7112  df-fin 7113  df-oi 7479  df-cnf 7617
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