Theorem f1ofun 2802

Description: A one-to-one onto mapping is a function.

Assertion

Ref	Expression
f1ofun	⊢ (F:A–1-1-onto→B → Fun F)

Proof of Theorem f1ofun

Step	Hyp	Ref	Expression
1		f1ofn 2801	. 2 ⊢ (F:A–1-1-onto→B → F Fn A)
2		fnfun 2721	. 2 ⊢ (F Fn A → Fun F)
3	1, 2	syl 12	1 ⊢ (F:A–1-1-onto→B → Fun F)

Syntax hints:   → wi 2  Fun wfun 2416   Fn wfn 2417  –1-1-onto→wf1o 2421

This theorem is referenced by:  f1orel 2803  f1ocnvfv1 2919  f1ocnvfv2 2920  isotr 2935  isotrALT 2936  isofrlem 2939  mapenlem1 3384  php3 3411  uzrdgval 4657

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-fn 2433  df-f 2434  df-f1 2435  df-f1o 2437

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