Theorem con1b 334

Description: Contraposition. Bidirectional version of con1 131. (Contributed by NM, 3-Jan-1993.)

Assertion

Ref	Expression
con1b	|- ( ( -. ph -> ps ) <-> ( -. ps -> ph ) )

Proof of Theorem con1b

Step	Hyp	Ref	Expression
1		con1 131	. 2 |- ( ( -. ph -> ps ) -> ( -. ps -> ph ) )
2		con1 131	. 2 |- ( ( -. ps -> ph ) -> ( -. ph -> ps ) )
3	1, 2	impbii 190	1 |- ( ( -. ph -> ps ) <-> ( -. ps -> ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 187

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 188

This theorem is referenced by:  eximal  1662  r19.23v  2912  pwssun  4760  ist1-2  20294  cmpfi  20354  dchrelbas2  24028