Theorem pm3.31 432

Description: Theorem *3.31 (Imp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)

Assertion

Ref	Expression
pm3.31	|- ((ph -> (ps -> ch)) -> ((ph /\ ps) -> ch))

Proof of Theorem pm3.31

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ((ph -> (ps -> ch)) -> (ph -> (ps -> ch)))
2	1	imp3a 420	1 |- ((ph -> (ps -> ch)) -> ((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:  impexp  433  imp5a  581