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Theorem isoeq4 5705
 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 5357 . . 3
2 raleq 2626 . . . 4
32raleqbi1dv 2634 . . 3
41, 3anbi12d 464 . 2
5 df-isom 5132 . 2
6 df-isom 5132 . 2
74, 5, 63bitr4g 222 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331  wral 2416   class class class wbr 3929  wf1o 5122  cfv 5123   wiso 5124 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-fn 5126  df-f 5127  df-f1 5128  df-fo 5129  df-f1o 5130  df-isom 5132 This theorem is referenced by:  zfz1isolem1  10590  zfz1iso  10591  summodclem2a  11157  prodmodclem2a  11352
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