Theorem f1of 5287

Description: A one-to-one onto mapping is a mapping. (Contributed by set.mm contributors, 12-Dec-2003.)

Assertion

Ref	Expression
f1of	⊢ (F:A–1-1-onto→B → F:A–→B)

Proof of Theorem f1of

Step	Hyp	Ref	Expression
1		f1of1 5286	. 2 ⊢ (F:A–1-1-onto→B → F:A–1-1→B)
2		f1f 5258	. 2 ⊢ (F:A–1-1→B → F:A–→B)
3	1, 2	syl 15	1 ⊢ (F:A–1-1-onto→B → F:A–→B)

Syntax hints:   → wi 4  –→wf 4777  –1-1→wf1 4778  –1-1-onto→wf1o 4780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-f1 4792  df-f1o 4794

This theorem is referenced by:  f1ofn  5288  f1imacnv  5302  fsn  5432  f1ocnvfv1  5476  f1ofveu  5480  f1ocnvdm  5481  isocnv  5491  isores2  5493  isotr  5495  f1oiso2  5500  mapsn  6026  enmap2lem5  6067  enmap1lem5  6073  1cnc  6139