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Theorem ffund 5947
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 5946 . 2 (𝐹:𝐴𝐵 → Fun 𝐹)
31, 2syl 17 1 (𝜑 → Fun 𝐹)
Colors of variables: wff setvar class
Syntax hints:  wi 4  Fun wfun 5783  wf 5785
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 195  df-an 384  df-fn 5792  df-f 5793
This theorem is referenced by:  fmptco  6287  evlslem3  19283  mdegldg  23574  gneispacefun  37238  subsaliuncllem  39034  ovnovollem2  39330  preimaioomnf  39389  smfresal  39456  smfres  39458  smfco  39470  vdegp1bi-av  40734  1wlkreslem  40859  1wlkres  40860
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