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Theorem f1f 5258

Description: A one-to-one mapping is a mapping. (Contributed by set.mm contributors, 31-Dec-1996.)

**Assertion**
Ref	Expression
f1f	⊢ (F:A–1-1→B → F:A–→B)

**Proof of Theorem f1f**
Step	Hyp	Ref	Expression
1		df-f1 4792	. 2 ⊢ (F:A–1-1→B ↔ (F:A–→B ∧ Fun ^◡F))
2	1	simplbi 446	1 ⊢ (F:A–1-1→B → F:A–→B)

Colors of variables: wff setvar class

Syntax hints: → wi 4 ^◡ccnv 4771 Fun wfun 4775 –→wf 4777 –1-1→wf1 4778

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

This theorem is referenced by: f1fn 5259 f1ss 5262 f1of 5287 dff1o5 5295 fun11iun 5305 dflec3 6221