f1of - New Foundations Explorer

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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)

Colors of variables: wff setvar class

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

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