Theorem pm3.31 249

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	impd 242	1 |- ( ( ph -> ( ps -> ch ) ) -> ( ( ph /\ ps ) -> ch ) )

Syntax hints:   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100

This theorem is referenced by:  impexp  250  imp5a  340  equsexd  1617  mo3h  1953  rexim  2413  peano5  4321  issref  4707  bj-indind  10056  peano5setOLD  10065