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Theorem ffund 5962
 Description: A mapping is a function, deduction version. (Contributed by Glauco Siliprandi, 3-Mar-2021.)
Hypothesis
Ref Expression
ffund.1 (𝜑𝐹:𝐴𝐵)
Assertion
Ref Expression
ffund (𝜑 → Fun 𝐹)

Proof of Theorem ffund
StepHypRef Expression
1 ffund.1 . 2 (𝜑𝐹:𝐴𝐵)
2 ffun 5961 . 2 (𝐹:𝐴𝐵 → Fun 𝐹)
31, 2syl 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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