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Theorem isoeq4 6042
 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 5666 . . 3
2 raleq 2904 . . . 4
32raleqbi1dv 2912 . . 3
41, 3anbi12d 692 . 2
5 df-isom 5463 . 2
6 df-isom 5463 . 2
74, 5, 63bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652  wral 2705   class class class wbr 4212  wf1o 5453  cfv 5454   wiso 5455 This theorem is referenced by:  oieu  7508  oiid  7510  finnisoeu  7994  iunfictbso  7995  fz1isolem  11710  isercolllem3  12460  summolem2a  12509  erdszelem1  24877  erdsze  24888  erdsze2lem1  24889  erdsze2lem2  24890  prodmolem2a  25260 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-fn 5457  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461  df-isom 5463
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