Theorem impcon4bid 196

Description: A variation on impbid 183 with contraposition. (Contributed by Jeff Hankins, 3-Jul-2009.)

Hypotheses

Ref	Expression
impcon4bid.1	|- (ph -> (ps -> ch))
impcon4bid.2	|- (ph -> (-. ps -> -. ch))

Assertion

Ref	Expression
impcon4bid	|- (ph -> (ps <-> ch))

Proof of Theorem impcon4bid

Step	Hyp	Ref	Expression
1		impcon4bid.1	. 2 |- (ph -> (ps -> ch))
2		impcon4bid.2	. . 3 |- (ph -> (-. ps -> -. ch))
3	2	con4d 97	. 2 |- (ph -> (ch -> ps))
4	1, 3	impbid 183	1 |- (ph -> (ps <-> ch))

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:  con4bid  284