Theorem bnj930 32041

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 6452	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
3	1, 2	syl 17	1 ⊢ (𝜑 → Fun 𝐹)

Syntax hints:   → wi 4  Fun wfun 6348   Fn wfn 6349

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 209  df-an 399  df-fn 6357

This theorem is referenced by:  bnj945  32045  bnj545  32167  bnj548  32169  bnj553  32170  bnj570  32177  bnj929  32208  bnj966  32216  bnj1442  32321  bnj1450  32322  bnj1501  32339