Theorem f1eq3 5783

Description: Equality theorem for one-to-one functions. (Contributed by NM, 10-Feb-1997.)

Assertion

Ref	Expression
f1eq3

Proof of Theorem f1eq3

Step	Hyp	Ref	Expression
1		feq3 5720	. . 3
2	1	anbi1d 704	. 2
3		df-f1 5598	. 2
4		df-f1 5598	. 2
5	2, 3, 4	3bitr4g 288	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  `'ccnv 5003  Funwfun 5587  -->wf 5589  -1-1->wf1 5590

This theorem is referenced by:  f1oeq3  5814  f1eq123d  5816  tposf12  6999  brdomg  7546  pwfseq  9063  f1linds  18860  isuslgra  24343  isusgra  24344  isusgra0  24347  usgraop  24350  cusgraexilem2  24467  diaf1oN  36857

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-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-in 3482  df-ss 3489  df-f 5597  df-f1 5598