Theorem bnj930 31349

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)

Hypothesis

Ref	Expression
bnj930.1	⊢ (𝜑 → 𝐹 Fn 𝐴)

Assertion

Ref	Expression
bnj930	⊢ (𝜑 → Fun 𝐹)

Proof of Theorem bnj930

Step	Hyp	Ref	Expression
1		bnj930.1	. 2 ⊢ (𝜑 → 𝐹 Fn 𝐴)
2		fnfun 6197	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
3	1, 2	syl 17	1 ⊢ (𝜑 → Fun 𝐹)

Syntax hints:   → wi 4  Fun wfun 6093   Fn wfn 6094

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 199  df-an 386  df-fn 6102

This theorem is referenced by:  bnj945  31353  bnj545  31474  bnj548  31476  bnj553  31477  bnj570  31484  bnj929  31515  bnj966  31523  bnj1442  31626  bnj1450  31627  bnj1501  31644