Theorem pm5.31 346

Description: Theorem *5.31 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.31	|- ( ( ch /\ ( ph -> ps ) ) -> ( ph -> ( ps /\ ch ) ) )

Proof of Theorem pm5.31

Step	Hyp	Ref	Expression
1		pm3.21 262	. . 3 |- ( ch -> ( ps -> ( ps /\ ch ) ) )
2	1	imim2d 54	. 2 |- ( ch -> ( ( ph -> ps ) -> ( ph -> ( ps /\ ch ) ) ) )
3	2	imp 123	1 |- ( ( ch /\ ( ph -> ps ) ) -> ( ph -> ( ps /\ ch ) ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by: (None)