Theorem pm2.61dc 762

Description: Case elimination for a decidable proposition. Based on theorem *2.61 of [WhiteheadRussell] p. 107. (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 759	. 2 |- (DECID ph -> ( ( -. ph -> ps ) -> ( ( ph -> ps ) -> ps ) ) )
2	1	com23 72	1 |- (DECID ph -> ( ( ph -> ps ) -> ( ( -. ph -> ps ) -> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4  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-io 630

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

This theorem is referenced by: (None)