Theorem expdcom 1371

Description: Commuted form of expd 254. (Contributed by Alan Sare, 18-Mar-2012.)

Hypothesis

Ref	Expression
expdcom.1	|- ( ph -> ( ( ps /\ ch ) -> th ) )

Assertion

Ref	Expression
expdcom	|- ( ps -> ( ch -> ( ph -> th ) ) )

Proof of Theorem expdcom

Step	Hyp	Ref	Expression
1		expdcom.1	. . 3 |- ( ph -> ( ( ps /\ ch ) -> th ) )
2	1	expd 254	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	com3l 80	1 |- ( ps -> ( ch -> ( ph -> th ) ) )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106

This theorem is referenced by:  nndi  6088  nnmass  6089  mulexp  9515  expadd  9518  expmul  9521