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Theorem isoeq4 5444
 Description: Equality theorem for isomorphisms. (Contributed by NM, 17-May-2004.)
Assertion
Ref Expression
isoeq4

Proof of Theorem isoeq4
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 f1oeq2 5118 . . 3
2 raleq 2505 . . . 4
32raleqbi1dv 2513 . . 3
41, 3anbi12d 442 . 2
5 df-isom 4911 . 2
6 df-isom 4911 . 2
74, 5, 63bitr4g 212 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98   wceq 1243  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-tru 1246  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-fn 4905  df-f 4906  df-f1 4907  df-fo 4908  df-f1o 4909  df-isom 4911 This theorem is referenced by: (None)
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