Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ffun | GIF version |
Description: A mapping is a function. (Contributed by NM, 3-Aug-1994.) |
Ref | Expression |
---|---|
ffun | ⊢ (𝐹:𝐴⟶𝐵 → Fun 𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffn 5066 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
2 | fnfun 5016 | . 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝐹:𝐴⟶𝐵 → Fun 𝐹) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Fun wfun 4916 Fn wfn 4917 ⟶wf 4918 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 |
This theorem depends on definitions: df-bi 115 df-fn 4925 df-f 4926 |
This theorem is referenced by: funssxp 5080 f00 5101 fofun 5127 fun11iun 5167 fimacnv 5317 dff3im 5333 fmptco 5351 fliftf 5459 smores2 5932 ac6sfi 6379 nn0supp 8340 climdm 10134 |
Copyright terms: Public domain | W3C validator |