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Mirrors > Home > MPE Home > Th. List > ffund | Structured version Visualization version 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 5961 | . 2 ⊢ (𝐹:𝐴⟶𝐵 → Fun 𝐹) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → Fun 𝐹) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 Fun wfun 5798 ⟶wf 5800 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 df-fn 5807 df-f 5808 |
This theorem is referenced by: fmptco 6303 evlslem3 19335 mdegldg 23630 gneispacefun 37455 subsaliuncllem 39251 ovnovollem2 39547 preimaioomnf 39606 smfresal 39673 smfres 39675 smfco 39687 vdegp1bi-av 40753 1wlkreslem 40878 1wlkres 40879 |
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