Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > funfnd | GIF version |
Description: A function is a function over its domain. (Contributed by Glauco Siliprandi, 23-Oct-2021.) |
Ref | Expression |
---|---|
funfnd.1 | ⊢ (𝜑 → Fun 𝐴) |
Ref | Expression |
---|---|
funfnd | ⊢ (𝜑 → 𝐴 Fn dom 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | funfnd.1 | . 2 ⊢ (𝜑 → Fun 𝐴) | |
2 | funfn 5218 | . 2 ⊢ (Fun 𝐴 ↔ 𝐴 Fn dom 𝐴) | |
3 | 1, 2 | sylib 121 | 1 ⊢ (𝜑 → 𝐴 Fn dom 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 dom cdm 4604 Fun wfun 5182 Fn wfn 5183 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-gen 1437 ax-ext 2147 |
This theorem depends on definitions: df-bi 116 df-cleq 2158 df-fn 5191 |
This theorem is referenced by: ennnfonelemf1 12351 dvfgg 13297 |
Copyright terms: Public domain | W3C validator |