Theorem con2b 659

Description: Contraposition. Bidirectional version of con2 633. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
con2b	|- ( ( ph -> -. ps ) <-> ( ps -> -. ph ) )

Proof of Theorem con2b

Step	Hyp	Ref	Expression
1		con2 633	. 2 |- ( ( ph -> -. ps ) -> ( ps -> -. ph ) )
2		con2 633	. 2 |- ( ( ps -> -. ph ) -> ( ph -> -. ps ) )
3	1, 2	impbii 125	1 |- ( ( ph -> -. ps ) <-> ( ps -> -. ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  mt2bi  674  pm4.15  684  dfdif3  3232  ssconb  3255  disjsn  3638  isprm3  12050