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Mirrors > Home > NFE Home > Th. List > f1of1 | GIF version |
Description: A one-to-one onto mapping is a one-to-one mapping. (Contributed by set.mm contributors, 12-Dec-2003.) |
Ref | Expression |
---|---|
f1of1 | ⊢ (F:A–1-1-onto→B → F:A–1-1→B) |
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 |
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