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Theorem isocnv3 6054
 Description: Complementation law for isomorphism. (Contributed by Mario Carneiro, 9-Sep-2015.)
Hypotheses
Ref Expression
isocnv3.1
isocnv3.2
Assertion
Ref Expression
isocnv3

Proof of Theorem isocnv3
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 brxp 4911 . . . . . . . 8
2 isocnv3.1 . . . . . . . . . . 11
32breqi 4220 . . . . . . . . . 10
4 brdif 4262 . . . . . . . . . 10
53, 4bitri 242 . . . . . . . . 9
65baib 873 . . . . . . . 8
71, 6sylbir 206 . . . . . . 7
87adantl 454 . . . . . 6
9 f1of 5676 . . . . . . . 8
10 ffvelrn 5870 . . . . . . . . . 10
11 ffvelrn 5870 . . . . . . . . . 10
1210, 11anim12dan 812 . . . . . . . . 9
13 brxp 4911 . . . . . . . . 9
1412, 13sylibr 205 . . . . . . . 8
159, 14sylan 459 . . . . . . 7
16 isocnv3.2 . . . . . . . . . 10
1716breqi 4220 . . . . . . . . 9
18 brdif 4262 . . . . . . . . 9
1917, 18bitri 242 . . . . . . . 8
2019baib 873 . . . . . . 7
2115, 20syl 16 . . . . . 6
228, 21bibi12d 314 . . . . 5
23 notbi 288 . . . . 5
2422, 23syl6rbbr 257 . . . 4
25242ralbidva 2747 . . 3
2625pm5.32i 620 . 2
27 df-isom 5465 . 2
28 df-isom 5465 . 2
2926, 27, 283bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 178   wa 360   wceq 1653   wcel 1726  wral 2707   cdif 3319   class class class wbr 4214   cxp 4878  wf 5452  wf1o 5455  cfv 5456   wiso 5457 This theorem is referenced by:  leiso  11710  gtiso  24090 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  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-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-rn 4891  df-iota 5420  df-fun 5458  df-fn 5459  df-f 5460  df-f1 5461  df-f1o 5463  df-fv 5464  df-isom 5465
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