Theorem fnfund 6655

Description: A function with domain is a function, deduction form. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypothesis

Ref	Expression
fnfund.1	⊢ (𝜑 → 𝐹 Fn 𝐴)

Assertion

Ref	Expression
fnfund	⊢ (𝜑 → Fun 𝐹)

Proof of Theorem fnfund

Step	Hyp	Ref	Expression
1		fnfund.1	. 2 ⊢ (𝜑 → 𝐹 Fn 𝐴)
2		fnfun 6654	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
3	1, 2	syl 17	1 ⊢ (𝜑 → Fun 𝐹)

Syntax hints:   → wi 4  Fun wfun 6542   Fn wfn 6543

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 206  df-an 396  df-fn 6551

This theorem is referenced by:  imadrhmcl  20685  noseqrdg0  28193  noseqrdgsuc  28194  ply1degltdimlem  33320  bnj945  34404  bnj545  34526  bnj548  34528  bnj553  34529  bnj570  34536  bnj929  34567  bnj966  34575  bnj1442  34680  bnj1450  34681  bnj1501  34698  aks6d1c2lem4  41598  aks6d1c2  41601  aks6d1c6lem5  41649  eqresfnbd  41723