Theorem con5 38728

Description: Biconditional contraposition variation. This proof is con5VD 39136 automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
con5	|- ( ( ph <-> -. ps ) -> ( -. ph -> ps ) )

Proof of Theorem con5

Step	Hyp	Ref	Expression
1		biimpr 210	. 2 |- ( ( ph <-> -. ps ) -> ( -. ps -> ph ) )
2	1	con1d 139	1 |- ( ( ph <-> -. ps ) -> ( -. ph -> ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197

This theorem is referenced by:  con5i  38729