Theorem isoeq3 6217

Description: Equality theorem for isomorphisms. (Contributed by NM, 17-May-2004.)

Assertion

Ref	Expression
isoeq3

Proof of Theorem isoeq3

Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		breq 4454	. . . . 5
2	1	bibi2d 318	. . . 4
3	2	2ralbidv 2901	. . 3
4	3	anbi2d 703	. 2
5		df-isom 5602	. 2
6		df-isom 5602	. 2
7	4, 5, 6	3bitr4g 288	1

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  Isomwiso 5594

This theorem is referenced by:  fnwelem  6915  hartogslem1  7988  leiso  12508  gtiso  27519

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-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-cleq 2449  df-clel 2452  df-ral 2812  df-br 4453  df-isom 5602