Theorem con34b 283

Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
con34b	|- ((ph -> ps) <-> (-. ps -> -. ph))

Proof of Theorem con34b

Step	Hyp	Ref	Expression
1		con3 126	. 2 |- ((ph -> ps) -> (-. ps -> -. ph))
2		ax-3 8	. 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:  mtt  329  pm4.14  561  sscon34  3662  evenodddisjlem1  4516