Theorem bnj930 30094

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 5902	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
3	1, 2	syl 17	1 ⊢ (𝜑 → Fun 𝐹)

Syntax hints:   → wi 4  Fun wfun 5798   Fn wfn 5799

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 196  df-an 385  df-fn 5807

This theorem is referenced by:  bnj945  30098  bnj545  30219  bnj548  30221  bnj553  30222  bnj570  30229  bnj929  30260  bnj966  30268  bnj1442  30371  bnj1450  30372  bnj1501  30389