Theorem bnj930 30840

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

Hypothesis

Ref	Expression
bnj930.1	|- ( ph -> F Fn A )

Assertion

Ref	Expression
bnj930	|- ( ph -> Fun F )

Proof of Theorem bnj930

Step	Hyp	Ref	Expression
1		bnj930.1	. 2 |- ( ph -> F Fn A )
2		fnfun 5988	. 2 |- ( F Fn A -> Fun F )
3	1, 2	syl 17	1 |- ( ph -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5882   Fn wfn 5883

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 197  df-an 386  df-fn 5891

This theorem is referenced by:  bnj945  30844  bnj545  30965  bnj548  30967  bnj553  30968  bnj570  30975  bnj929  31006  bnj966  31014  bnj1442  31117  bnj1450  31118  bnj1501  31135