Theorem pm2.26dc 892

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 40	. 2 |- ( ph -> ( ( ph -> ps ) -> ps ) )
2		imordc 882	. 2 |- (DECID ph -> ( ( ph -> ( ( ph -> ps ) -> ps ) ) <-> ( -. ph \/ ( ( ph -> ps ) -> ps ) ) ) )
3	1, 2	mpbii 147	1 |- (DECID ph -> ( -. ph \/ ( ( ph -> ps ) -> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 697  DECID wdc 819

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 603  ax-in2 604  ax-io 698

This theorem depends on definitions:  df-bi 116  df-dc 820

This theorem is referenced by: (None)