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Mirrors > Home > ILE Home > Th. List > ffnd | GIF version |
Description: A mapping is a function with domain, deduction form. (Contributed by Glauco Siliprandi, 17-Aug-2020.) |
Ref | Expression |
---|---|
ffnd.1 | ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) |
Ref | Expression |
---|---|
ffnd | ⊢ (𝜑 → 𝐹 Fn 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffnd.1 | . 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | |
2 | ffn 5161 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → 𝐹 Fn 𝐴) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Fn wfn 5010 ⟶wf 5011 |
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-f 5019 |
This theorem is referenced by: seq3feq2 9893 ser0f 9950 resunimafz0 10236 seq3shft 10272 fisumss 10784 efcvgfsum 10957 nninfalllemn 11898 nninfall 11900 nninfsellemeqinf 11908 |
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