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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 5046 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
2 | fnfun 4996 | . 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 4896 Fn wfn 4897 ⟶wf 4898 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 |
This theorem depends on definitions: df-bi 110 df-fn 4905 df-f 4906 |
This theorem is referenced by: funssxp 5060 f00 5081 fofun 5107 fun11iun 5147 fimacnv 5296 dff3im 5312 fmptco 5330 fliftf 5439 smores2 5909 ac6sfi 6352 nn0supp 8234 climdm 9816 |
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