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Mirrors > Home > NFE Home > Th. List > funforn | GIF version |
Description: A function maps its domain onto its range. (Contributed by set.mm contributors, 23-Jul-2004.) |
Ref | Expression |
---|---|
funforn | ⊢ (Fun A ↔ A:dom A–onto→ran A) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funfn 5136 | . 2 ⊢ (Fun A ↔ A Fn dom A) | |
2 | dffn4 5275 | . 2 ⊢ (A Fn dom A ↔ A:dom A–onto→ran A) | |
3 | 1, 2 | bitri 240 | 1 ⊢ (Fun A ↔ A:dom A–onto→ran A) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 176 dom cdm 4772 ran crn 4773 Fun wfun 4775 Fn wfn 4776 –onto→wfo 4779 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-cleq 2346 df-fn 4790 df-fo 4793 |
This theorem is referenced by: (None) |
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