Theorem pm3.31 461

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 22	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ph -> ( ps -> ch ) ) )
2	1	impd 447	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ( 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:  impexp  462  imp5a  624  issref  5509  bj-sb56  32639  bj-ssbequ2  32643  trsbc  38750  3impexpVD  39091  trsbcVD  39113  19.41rgVD  39138  stoweidlem17  40234