Theorem f1of 5288

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 5287	. 2 |- (F:A-1-1-onto->B -> F:A-1-1->B)
2		f1f 5259	. 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 4778  -1-1->wf1 4779  -1-1-onto->wf1o 4781

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 4793  df-f1o 4795

This theorem is referenced by:  f1ofn  5289  f1imacnv  5303  fsn  5433  f1ocnvfv1  5477  f1ofveu  5481  f1ocnvdm  5482  isocnv  5492  isores2  5494  isotr  5496  f1oiso2  5501  mapsn  6027  enmap2lem5  6068  enmap1lem5  6074  1cnc  6140