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Mirrors > Home > ILE Home > Th. List > ffund | GIF version |
Description: A mapping is a function, deduction version. (Contributed by Glauco Siliprandi, 3-Mar-2021.) |
Ref | Expression |
---|---|
ffund.1 | ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) |
Ref | Expression |
---|---|
ffund | ⊢ (𝜑 → Fun 𝐹) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ffund.1 | . 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵) | |
2 | ffun 5275 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → Fun 𝐹) | |
3 | 1, 2 | syl 14 | 1 ⊢ (𝜑 → Fun 𝐹) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Fun wfun 5117 ⟶wf 5119 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 |
This theorem depends on definitions: df-bi 116 df-fn 5126 df-f 5127 |
This theorem is referenced by: ennnfonelemrnh 11934 ennnfonelemf1 11936 ctinfomlemom 11945 cncnp 12404 txcnp 12445 dvidlemap 12834 dvaddxx 12841 dvmulxx 12842 dvcjbr 12846 dvcj 12847 dvrecap 12851 |
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