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Theorem isocnv2 6051
 Description: Converse law for isomorphism. (Contributed by Mario Carneiro, 30-Jan-2014.)
Assertion
Ref Expression
isocnv2

Proof of Theorem isocnv2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 ralcom 2868 . . . 4
2 vex 2959 . . . . . . 7
3 vex 2959 . . . . . . 7
42, 3brcnv 5055 . . . . . 6
5 fvex 5742 . . . . . . 7
6 fvex 5742 . . . . . . 7
75, 6brcnv 5055 . . . . . 6
84, 7bibi12i 307 . . . . 5
982ralbii 2731 . . . 4
101, 9bitr4i 244 . . 3
1110anbi2i 676 . 2
12 df-isom 5463 . 2
13 df-isom 5463 . 2
1411, 12, 133bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wral 2705   class class class wbr 4212  ccnv 4877  wf1o 5453  cfv 5454   wiso 5455 This theorem is referenced by:  wofib  7514  leiso  11708  gtiso  24088 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-cnv 4886  df-iota 5418  df-fv 5462  df-isom 5463
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