Theorem con34bdc 799

Description: Contraposition. Theorem *4.1 of [WhiteheadRussell] p. 116, but for a decidable proposition. (Contributed by Jim Kingdon, 24-Apr-2018.)

Assertion

Ref	Expression
con34bdc	|- (DECID ps -> ( ( ph -> ps ) <-> ( -. ps -> -. ph ) ) )

Proof of Theorem con34bdc

Step	Hyp	Ref	Expression
1		con3 604	. 2 |- ( ( ph -> ps ) -> ( -. ps -> -. ph ) )
2		condc 783	. 2 |- (DECID ps -> ( ( -. ps -> -. ph ) -> ( ph -> ps ) ) )
3	1, 2	impbid2 141	1 |- (DECID ps -> ( ( ph -> ps ) <-> ( -. ps -> -. ph ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 103  DECID wdc 776

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663

This theorem depends on definitions:  df-bi 115  df-dc 777

This theorem is referenced by:  pm4.14dc  821  algcvgblem  10638