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Theorem isocnv3 6241
 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 4870 . . . . . . . 8
2 isocnv3.1 . . . . . . . . . . 11
32breqi 4401 . . . . . . . . . 10
4 brdif 4446 . . . . . . . . . 10
53, 4bitri 257 . . . . . . . . 9
65baib 919 . . . . . . . 8
71, 6sylbir 218 . . . . . . 7
87adantl 473 . . . . . 6
9 f1of 5828 . . . . . . . 8
10 ffvelrn 6035 . . . . . . . . . 10
11 ffvelrn 6035 . . . . . . . . . 10
1210, 11anim12dan 855 . . . . . . . . 9
13 brxp 4870 . . . . . . . . 9
1412, 13sylibr 217 . . . . . . . 8
159, 14sylan 479 . . . . . . 7
16 isocnv3.2 . . . . . . . . . 10
1716breqi 4401 . . . . . . . . 9
18 brdif 4446 . . . . . . . . 9
1917, 18bitri 257 . . . . . . . 8
2019baib 919 . . . . . . 7
2115, 20syl 17 . . . . . 6
228, 21bibi12d 328 . . . . 5
23 notbi 302 . . . . 5
2422, 23syl6rbbr 272 . . . 4
25242ralbidva 2831 . . 3
2625pm5.32i 649 . 2
27 df-isom 5598 . 2
28 df-isom 5598 . 2
2926, 27, 283bitr4i 285 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 189   wa 376   wceq 1452   wcel 1904  wral 2756   cdif 3387   class class class wbr 4395   cxp 4837  wf 5585  wf1o 5588  cfv 5589   wiso 5590 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-opab 4455  df-id 4754  df-xp 4845  df-rel 4846  df-cnv 4847  df-co 4848  df-dm 4849  df-rn 4850  df-iota 5553  df-fun 5591  df-fn 5592  df-f 5593  df-f1 5594  df-f1o 5596  df-fv 5597  df-isom 5598 This theorem is referenced by:  leiso  12663  gtiso  28356
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