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Theorem isores2 6053
 Description: An isomorphism from one well-order to another can be restricted on either well-order. (Contributed by Mario Carneiro, 15-Jan-2013.)
Assertion
Ref Expression
isores2

Proof of Theorem isores2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 f1of 5674 . . . . . . . 8
2 ffvelrn 5868 . . . . . . . . . 10
32adantrr 698 . . . . . . . . 9
4 ffvelrn 5868 . . . . . . . . . 10
54adantrl 697 . . . . . . . . 9
6 brinxp 4940 . . . . . . . . 9
73, 5, 6syl2anc 643 . . . . . . . 8
81, 7sylan 458 . . . . . . 7
98anassrs 630 . . . . . 6
109bibi2d 310 . . . . 5
1110ralbidva 2721 . . . 4
1211ralbidva 2721 . . 3
1312pm5.32i 619 . 2
14 df-isom 5463 . 2
15 df-isom 5463 . 2
1613, 14, 153bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wcel 1725  wral 2705   cin 3319   class class class wbr 4212   cxp 4876  wf 5450  wf1o 5453  cfv 5454   wiso 5455 This theorem is referenced by:  isores1  6054  hartogslem1  7511  leiso  11708  icopnfhmeo  18968  iccpnfhmeo  18970  gtiso  24088  xrge0iifhmeo  24322 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  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-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-f1o 5461  df-fv 5462  df-isom 5463
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