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Theorem isoeq1 6215
 Description: Equality theorem for isomorphisms. (Contributed by NM, 17-May-2004.)
Assertion
Ref Expression
isoeq1

Proof of Theorem isoeq1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 f1oeq1 5812 . . 3
2 fveq1 5870 . . . . . 6
3 fveq1 5870 . . . . . 6
42, 3breq12d 4465 . . . . 5
54bibi2d 318 . . . 4
652ralbidv 2901 . . 3
71, 6anbi12d 710 . 2
8 df-isom 5602 . 2
9 df-isom 5602 . 2
107, 8, 93bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  A.wral 2807   class class class wbr 4452  -1-1-onto->wf1o 5592  cfv 5593  Isom`wiso 5594 This theorem is referenced by:  isores1  6230  wemoiso  6785  wemoiso2  6786  ordiso  7962  oieu  7985  finnisoeu  8515  iunfictbso  8516  infmsup  10546  ltweuz  12072  fz1isolem  12510  isercolllem2  13488  isercoll  13490  dvgt0lem2  22404  efcvx  22844  relogiso  22982  logccv  23044  erdszelem1  28635  erdsze  28646  erdsze2lem2  28648  fzisoeu  31500  fourierdlem36  31925  fourierdlem96  31985  fourierdlem97  31986  fourierdlem98  31987  fourierdlem99  31988  fourierdlem105  31994  fourierdlem106  31995  fourierdlem108  31997  fourierdlem110  31999  fourierdlem112  32001  fourierdlem113  32002  fourierdlem115  32004 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-iota 5556  df-fun 5595  df-fn 5596  df-f 5597  df-f1 5598  df-fo 5599  df-f1o 5600  df-fv 5601  df-isom 5602
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