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Theorem cardval2 7883
 Description: An alternate version of the value of the cardinal number of a set. Compare cardval 8426. This theorem could be used to give us a simpler definition of in place of df-card 7831. It apparently does not occur in the literature. (Contributed by NM, 7-Nov-2003.)
Assertion
Ref Expression
cardval2
Distinct variable group:   ,

Proof of Theorem cardval2
StepHypRef Expression
1 cardsdomel 7866 . . . . . 6
21ancoms 441 . . . . 5
32pm5.32da 624 . . . 4
4 cardon 7836 . . . . . 6
54oneli 4692 . . . . 5
65pm4.71ri 616 . . . 4
73, 6syl6rbbr 257 . . 3
87abbi2dv 2553 . 2
9 df-rab 2716 . 2
108, 9syl6eqr 2488 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  cab 2424  crab 2711   class class class wbr 4215  con0 4584   cdm 4881  cfv 5457   csdm 7111  ccrd 7827 This theorem is referenced by:  ondomon  8443  alephsuc3  8460 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pow 4380  ax-pr 4406  ax-un 4704 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-pss 3338  df-nul 3631  df-if 3742  df-pw 3803  df-sn 3822  df-pr 3823  df-tp 3824  df-op 3825  df-uni 4018  df-int 4053  df-br 4216  df-opab 4270  df-mpt 4271  df-tr 4306  df-eprel 4497  df-id 4501  df-po 4506  df-so 4507  df-fr 4544  df-we 4546  df-ord 4587  df-on 4588  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fun 5459  df-fn 5460  df-f 5461  df-f1 5462  df-fo 5463  df-f1o 5464  df-fv 5465  df-er 6908  df-en 7113  df-dom 7114  df-sdom 7115  df-card 7831
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