Theorem pm2.61dc 855

Description: Case elimination for a decidable proposition. Theorem *2.61 of [WhiteheadRussell] p. 107 under a decidability condition. (Contributed by Jim Kingdon, 29-Mar-2018.)

Assertion

Ref	Expression
pm2.61dc	|- (DECID ph -> ( ( ph -> ps ) -> ( ( -. ph -> ps ) -> ps ) ) )

Proof of Theorem pm2.61dc

Step	Hyp	Ref	Expression
1		pm2.6dc 852	. 2 |- (DECID ph -> ( ( -. ph -> ps ) -> ( ( ph -> ps ) -> ps ) ) )
2	1	com23 78	1 |- (DECID ph -> ( ( ph -> ps ) -> ( ( -. ph -> ps ) -> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4  DECID wdc 824

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-io 699

This theorem depends on definitions:  df-bi 116  df-dc 825

This theorem is referenced by: (None)