Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfoi Structured version   Unicode version

Theorem nfoi 7486
 Description: Hypothesis builder for ordinal isomorphism. (Contributed by Mario Carneiro, 23-May-2015.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
nfoi.1
nfoi.2
Assertion
Ref Expression
nfoi OrdIso

Proof of Theorem nfoi
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-oi 7482 . 2 OrdIso Se recs recs
2 nfoi.1 . . . . 5
3 nfoi.2 . . . . 5
42, 3nfwe 4561 . . . 4
52, 3nfse 4560 . . . 4 Se
64, 5nfan 1847 . . 3 Se
7 nfcv 2574 . . . . . 6
8 nfcv 2574 . . . . . . . . . 10
9 nfcv 2574 . . . . . . . . . . 11
10 nfcv 2574 . . . . . . . . . . 11
119, 2, 10nfbr 4259 . . . . . . . . . 10
128, 11nfral 2761 . . . . . . . . 9
1312, 3nfrab 2891 . . . . . . . 8
14 nfcv 2574 . . . . . . . . . 10
15 nfcv 2574 . . . . . . . . . 10
1614, 2, 15nfbr 4259 . . . . . . . . 9
1716nfn 1812 . . . . . . . 8
1813, 17nfral 2761 . . . . . . 7
1918, 13nfriota 6562 . . . . . 6
207, 19nfmpt 4300 . . . . 5
2120nfrecs 6638 . . . 4 recs
22 nfcv 2574 . . . . . . . 8
2321, 22nfima 5214 . . . . . . 7 recs
24 nfcv 2574 . . . . . . . 8
25 nfcv 2574 . . . . . . . 8
2624, 2, 25nfbr 4259 . . . . . . 7
2723, 26nfral 2761 . . . . . 6 recs
283, 27nfrex 2763 . . . . 5 recs
29 nfcv 2574 . . . . 5
3028, 29nfrab 2891 . . . 4 recs
3121, 30nfres 5151 . . 3 recs recs
32 nfcv 2574 . . 3
336, 31, 32nfif 3765 . 2 Se recs recs
341, 33nfcxfr 2571 1 OrdIso
 Colors of variables: wff set class Syntax hints:   wn 3   wa 360  wnfc 2561  wral 2707  wrex 2708  crab 2711  cvv 2958  c0 3630  cif 3741   class class class wbr 4215   cmpt 4269   Se wse 4542   wwe 4543  con0 4584   crn 4882   cres 4883  cima 4884  crio 6545  recscrecs 6635  OrdIsocoi 7481 This theorem is referenced by:  hsmexlem2  8312 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-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 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-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-reu 2714  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-mpt 4271  df-po 4506  df-so 4507  df-fr 4544  df-se 4545  df-we 4546  df-xp 4887  df-cnv 4889  df-dm 4891  df-rn 4892  df-res 4893  df-ima 4894  df-iota 5421  df-fv 5465  df-riota 6552  df-recs 6636  df-oi 7482
 Copyright terms: Public domain W3C validator