Theorem impcon4bid 217

Description: A variation on impbid 202 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 114	. 2 |- ( ph -> ( ch -> ps ) )
4	1, 3	impbid 202	1 |- ( ph -> ( ps <-> ch ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196

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 197

This theorem is referenced by:  con4bid  307  soisoi  6578  isomin  6587  alephdom  8904  nn0n0n1ge2b  11359  om2uzlt2i  12750  sadcaddlem  15179  isprm5  15419  pcdvdsb  15573  cvgdvgrat  38512