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Theorem isoeq4 5485
 Description: Equality theorem for isomorphisms. (Contributed by set.mm contributors, 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 5282 . . 3
2 raleq 2807 . . . 4
32raleqbi1dv 2815 . . 3
41, 3anbi12d 691 . 2
5 df-iso 4796 . 2
6 df-iso 4796 . 2
74, 5, 63bitr4g 279 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   wceq 1642  wral 2614   class class class wbr 4639  wf1o 4780  cfv 4781   wiso 4782 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-fn 4790  df-f 4791  df-f1 4792  df-fo 4793  df-f1o 4794  df-iso 4796 This theorem is referenced by: (None)
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