![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > funforn | GIF version |
Description: A function maps its domain onto its range. (Contributed by NM, 23-Jul-2004.) |
Ref | Expression |
---|---|
funforn | β’ (Fun π΄ β π΄:dom π΄βontoβran π΄) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funfn 5246 | . 2 β’ (Fun π΄ β π΄ Fn dom π΄) | |
2 | dffn4 5444 | . 2 β’ (π΄ Fn dom π΄ β π΄:dom π΄βontoβran π΄) | |
3 | 1, 2 | bitri 184 | 1 β’ (Fun π΄ β π΄:dom π΄βontoβran π΄) |
Colors of variables: wff set class |
Syntax hints: β wb 105 dom cdm 4626 ran crn 4627 Fun wfun 5210 Fn wfn 5211 βontoβwfo 5214 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-gen 1449 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 df-fn 5219 df-fo 5222 |
This theorem is referenced by: dvrecap 14147 |
Copyright terms: Public domain | W3C validator |