Theorem ffund 5407

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 5406	. 2 ⊢ (𝐹:𝐴⟶𝐵 → Fun 𝐹)
3	1, 2	syl 14	1 ⊢ (𝜑 → Fun 𝐹)

Syntax hints:   → wi 4  Fun wfun 5248  ⟶wf 5250

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This theorem depends on definitions:  df-bi 117  df-fn 5257  df-f 5258

This theorem is referenced by:  ennnfonelemrnh  12573  ennnfonelemf1  12575  ctinfomlemom  12584  psrbaglesuppg  14158  psrelbasfun  14161  cncnp  14398  txcnp  14439  dvidlemap  14845  dvaddxx  14852  dvmulxx  14853  dvcjbr  14857  dvcj  14858  dvrecap  14862  plyaddlem1  14893  plymullem1  14894