Theorem pm4.52im 739

Description: One direction of theorem *4.52 of [WhiteheadRussell] p. 120. The converse also holds in classical logic. (Contributed by Jim Kingdon, 27-Jul-2018.)

Assertion

Ref	Expression
pm4.52im	|- ( ( ph /\ -. ps ) -> -. ( -. ph \/ ps ) )

Proof of Theorem pm4.52im

Step	Hyp	Ref	Expression
1		annimim 675	. 2 |- ( ( ph /\ -. ps ) -> -. ( ph -> ps ) )
2		imorr 710	. 2 |- ( ( -. ph \/ ps ) -> ( ph -> ps ) )
3	1, 2	nsyl 617	1 |- ( ( ph /\ -. ps ) -> -. ( -. ph \/ ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 103   \/ wo 697

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  pm4.53r  740