Theorem con2 643

Description: Contraposition. Theorem *2.03 of [WhiteheadRussell] p. 100. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Feb-2013.)

Assertion

Ref	Expression
con2	|- ( ( ph -> -. ps ) -> ( ps -> -. ph ) )

Proof of Theorem con2

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ( ph -> -. ps ) -> ( ph -> -. ps ) )
2	1	con2d 624	1 |- ( ( ph -> -. ps ) -> ( ps -> -. ph ) )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 614  ax-in2 615

This theorem is referenced by:  con2b  669  const  852