Theorem pm2.26dc 846

Description: Decidable proposition version of theorem *2.26 of [WhiteheadRussell] p. 104. (Contributed by Jim Kingdon, 20-Apr-2018.)

Assertion

Ref	Expression
pm2.26dc	|- (DECID ph -> ( -. ph \/ ( ( ph -> ps ) -> ps ) ) )

Proof of Theorem pm2.26dc

Step	Hyp	Ref	Expression
1		pm2.27 39	. 2 |- ( ph -> ( ( ph -> ps ) -> ps ) )
2		imordc 829	. 2 |- (DECID ph -> ( ( ph -> ( ( ph -> ps ) -> ps ) ) <-> ( -. ph \/ ( ( ph -> ps ) -> ps ) ) ) )
3	1, 2	mpbii 146	1 |- (DECID ph -> ( -. ph \/ ( ( ph -> ps ) -> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 661  DECID wdc 775

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 576  ax-in2 577  ax-io 662

This theorem depends on definitions:  df-bi 115  df-dc 776

This theorem is referenced by: (None)