Theorem con2b 324

Description: Contraposition. Bidirectional version of con2 108. (Contributed by NM, 5-Aug-1993.)

Assertion

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

Proof of Theorem con2b

Step	Hyp	Ref	Expression
1		con2 108	. 2 |- ((ph -> -. ps) -> (ps -> -. ph))
2		con2 108	. 2 |- ((ps -> -. ph) -> (ph -> -. ps))
3	1, 2	impbii 180	1 |- ((ph -> -. ps) <-> (ps -> -. ph))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176

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 177

This theorem is referenced by:  mt2bi  328  pm4.15  564  nic-ax  1438  nic-axALT  1439  ssconb  3400  disjsn  3787  evenodddisj  4517