Theorem con1b 331

Description: Contraposition. Bidirectional version of con1 128. (Contributed by NM, 3-Jan-1993.)

Assertion

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

Proof of Theorem con1b

Step	Hyp	Ref	Expression
1		con1 128	. 2 |- ( ( -. ph -> ps ) -> ( -. ps -> ph ) )
2		con1 128	. 2 |- ( ( -. ps -> ph ) -> ( -. ph -> ps ) )
3	1, 2	impbii 188	1 |- ( ( -. ph -> ps ) <-> ( -. ps -> ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 184

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 185

This theorem is referenced by:  eximal  1620  r19.23v  2934  pwssun  4775  ist1-2  20018  cmpfi  20078  dchrelbas2  23713