Theorem ffund 5947

Description: A mapping is a function, deduction version. (Contributed by Glauco Siliprandi, 3-Mar-2021.)

Hypothesis

Ref	Expression
ffund.1	⊢ (𝜑 → 𝐹:𝐴⟶𝐵)

Assertion

Ref	Expression
ffund	⊢ (𝜑 → Fun 𝐹)

Proof of Theorem ffund

Step	Hyp	Ref	Expression
1		ffund.1	. 2 ⊢ (𝜑 → 𝐹:𝐴⟶𝐵)
2		ffun 5946	. 2 ⊢ (𝐹:𝐴⟶𝐵 → Fun 𝐹)
3	1, 2	syl 17	1 ⊢ (𝜑 → Fun 𝐹)

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