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Theorem f1of1 5286

Description: A one-to-one onto mapping is a one-to-one mapping. (Contributed by set.mm contributors, 12-Dec-2003.)

**Assertion**
Ref	Expression
f1of1	⊢ (F:A–1-1-onto→B → F:A–1-1→B)

**Proof of Theorem f1of1**
Step	Hyp	Ref	Expression
1		df-f1o 4794	. 2 ⊢ (F:A–1-1-onto→B ↔ (F:A–1-1→B ∧ F:A–onto→B))
2	1	simplbi 446	1 ⊢ (F:A–1-1-onto→B → F:A–1-1→B)

Colors of variables: wff setvar class

Syntax hints: → wi 4 –1-1→wf1 4778 –onto→wfo 4779 –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-f1o 4794

This theorem is referenced by: f1of 5287 isoini2 5498 f1oiso 5499 swapres 5512 enpw1 6062 enpw1pw 6075 ncdisjun 6136 dflec3 6221 nclenc 6222 lenc 6223