Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  isoeq2 Structured version   Unicode version

Theorem isoeq2 6042
 Description: Equality theorem for isomorphisms. (Contributed by NM, 17-May-2004.)
Assertion
Ref Expression
isoeq2

Proof of Theorem isoeq2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 breq 4216 . . . . 5
21bibi1d 312 . . . 4
322ralbidv 2749 . . 3
43anbi2d 686 . 2
5 df-isom 5465 . 2
6 df-isom 5465 . 2
74, 5, 63bitr4g 281 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653  wral 2707   class class class wbr 4214  wf1o 5455  cfv 5456   wiso 5457 This theorem is referenced by:  leiso  11710  gtiso  24090 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555  df-cleq 2431  df-clel 2434  df-ral 2712  df-br 4215  df-isom 5465
 Copyright terms: Public domain W3C validator