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Theorem isorel 5448
 Description: An isomorphism connects binary relations via its function values. (Contributed by NM, 27-Apr-2004.)
Assertion
Ref Expression
isorel

Proof of Theorem isorel
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-isom 4911 . . 3
21simprbi 260 . 2
3 breq1 3767 . . . 4
4 fveq2 5178 . . . . 5
54breq1d 3774 . . . 4
63, 5bibi12d 224 . . 3
7 breq2 3768 . . . 4
8 fveq2 5178 . . . . 5
98breq2d 3776 . . . 4
107, 9bibi12d 224 . . 3
116, 10rspc2v 2662 . 2
122, 11mpan9 265 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243   wcel 1393  wral 2306   class class class wbr 3764  wf1o 4901  cfv 4902   wiso 4903 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-iota 4867  df-fv 4910  df-isom 4911 This theorem is referenced by:  isoresbr  5449  isoini  5457  isopolem  5461  isosolem  5463  smoiso  5917  ordiso2  6357
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