Theorem pm2.26dc 813

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 35	. 2 |- ( ph -> ( ( ph -> ps ) -> ps ) )
2		imordc 796	. 2 |- (DECID ph -> ( ( ph -> ( ( ph -> ps ) -> ps ) ) <-> ( -. ph \/ ( ( ph -> ps ) -> ps ) ) ) )
3	1, 2	mpbii 136	1 |- (DECID ph -> ( -. ph \/ ( ( ph -> ps ) -> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 629  DECID wdc 742

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110  df-dc 743

This theorem is referenced by: (None)