Theorem pm4.81dc 903

Description: Theorem *4.81 of [WhiteheadRussell] p. 122, for decidable propositions. This one needs a decidability condition, but compare with pm4.8 702 which holds for all propositions. (Contributed by Jim Kingdon, 4-Jul-2018.)

Assertion

Ref	Expression
pm4.81dc	|- (DECID ph -> ( ( -. ph -> ph ) <-> ph ) )

Proof of Theorem pm4.81dc

Step	Hyp	Ref	Expression
1		pm2.18dc 850	. 2 |- (DECID ph -> ( ( -. ph -> ph ) -> ph ) )
2		pm2.24 616	. 2 |- ( ph -> ( -. ph -> ph ) )
3	1, 2	impbid1 141	1 |- (DECID ph -> ( ( -. ph -> ph ) <-> ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 104  DECID wdc 829

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610  ax-io 704

This theorem depends on definitions:  df-bi 116  df-stab 826  df-dc 830

This theorem is referenced by: (None)