Theorem pm5.31 571

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		pm3.21 435	. . 3 |- (ch -> (ps -> (ps /\ ch)))
2	1	imim2d 48	. 2 |- (ch -> ((ph -> ps) -> (ph -> (ps /\ ch))))
3	2	imp 418	1 |- ((ch /\ (ph -> ps)) -> (ph -> (ps /\ ch)))

Syntax hints:   -> wi 4   /\ wa 358

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 177  df-an 360

This theorem is referenced by: (None)