Theorem pm3.37 690

Description: Theorem *3.37 (Transp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm3.37	|- ( ( ( ph /\ ps ) -> ch ) -> ( ( ph /\ -. ch ) -> -. ps ) )

Proof of Theorem pm3.37

Step	Hyp	Ref	Expression
1		pm3.3 261	. . 3 |- ( ( ( ph /\ ps ) -> ch ) -> ( ph -> ( ps -> ch ) ) )
2		con3 643	. . 3 |- ( ( ps -> ch ) -> ( -. ch -> -. ps ) )
3	1, 2	syl6 33	. 2 |- ( ( ( ph /\ ps ) -> ch ) -> ( ph -> ( -. ch -> -. ps ) ) )
4	3	impd 254	1 |- ( ( ( ph /\ ps ) -> ch ) -> ( ( ph /\ -. ch ) -> -. ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem is referenced by:  ndvdssub  12112