Theorem f1ofn 2801

Description: A one-to-one onto mapping is function on its domain.

Assertion

Ref	Expression
f1ofn	|- (F:A-1-1-onto->B -> F Fn A)

Proof of Theorem f1ofn

Step	Hyp	Ref	Expression
1		f1of 2800	. 2 |- (F:A-1-1-onto->B -> F:A-->B)
2		ffn 2752	. 2 |- (F:A-->B -> F Fn A)
3	1, 2	syl 12	1 |- (F:A-1-1-onto->B -> F Fn A)

Syntax hints:   -> wi 2   Fn wfn 2417  -->wf 2418  -1-1-onto->wf1o 2421

This theorem is referenced by:  f1ofun 2802  isomin 2937  isoini 2938  isofrlem 2939  breng 3280  f1oeng 3298  phplem5 3407  php3 3411  unfilem3 3440  fiint 3445  facnnt 4870  ruclem6 4890

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-f 2434  df-f1 2435  df-f1o 2437

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