Theorem con2b 669

Description: Contraposition. Bidirectional version of con2 643. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem con2b

Step	Hyp	Ref	Expression
1		con2 643	. 2 |- ( ( ph -> -. ps ) -> ( ps -> -. ph ) )
2		con2 643	. 2 |- ( ( ps -> -. ph ) -> ( ph -> -. ps ) )
3	1, 2	impbii 126	1 |- ( ( ph -> -. ps ) <-> ( ps -> -. ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  mt2bi  684  pm4.15  694  dfdif3  3245  ssconb  3268  disjsn  3654  isprm3  12110