Theorem pm5.31 612

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		pm3.21 464	. . 3 |- ( ch -> ( ps -> ( ps /\ ch ) ) )
2	1	imim2d 57	. 2 |- ( ch -> ( ( ph -> ps ) -> ( ph -> ( ps /\ ch ) ) ) )
3	2	imp 445	1 |- ( ( ch /\ ( ph -> ps ) ) -> ( ph -> ( ps /\ ch ) ) )

Syntax hints:   -> wi 4   /\ wa 384

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

This theorem is referenced by:  bj-bary1lem1  33161