Theorem con3 637

Description: Contraposition. Theorem *2.16 of [WhiteheadRussell] p. 103. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 13-Feb-2013.)

Assertion

Ref	Expression
con3	|- ( ( ph -> ps ) -> ( -. ps -> -. ph ) )

Proof of Theorem con3

Step	Hyp	Ref	Expression
1		id 19	. 2 |- ( ( ph -> ps ) -> ( ph -> ps ) )
2	1	con3d 626	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 609  ax-in2 610

This theorem is referenced by:  mtt  680  annimim  681  pm3.37  684  con34bdc  866  hbnt  1646  ralf0  3518  ltleletr  8001  ltnsym  8005  bj-nnsn  13768  bj-nnclavius  13772  bj-con1st  13786