New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > ffun | GIF version |
Description: A mapping is a function. (Contributed by set.mm contributors, 3-Aug-1994.) |
Ref | Expression |
---|---|
ffun | ⊢ (F:A–→B → Fun F) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffn 5223 | . 2 ⊢ (F:A–→B → F Fn A) | |
2 | fnfun 5181 | . 2 ⊢ (F Fn A → Fun F) | |
3 | 1, 2 | syl 15 | 1 ⊢ (F:A–→B → Fun F) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 Fun wfun 4775 Fn wfn 4776 –→wf 4777 |
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-fn 4790 df-f 4791 |
This theorem is referenced by: funssxp 5233 f00 5249 fofun 5270 f1ores 5300 fimacnv 5411 dff3 5420 mapsspm 6021 xpsnen 6049 enprmaplem3 6078 |
Copyright terms: Public domain | W3C validator |