Theorem simprimdc 789

Description: Simplification given a decidable proposition. Similar to Theorem *3.27 (Simp) of [WhiteheadRussell] p. 112. (Contributed by Jim Kingdon, 30-Apr-2018.)

Assertion

Ref	Expression
simprimdc	|- (DECID ps -> ( -. ( ph -> -. ps ) -> ps ) )

Proof of Theorem simprimdc

Step	Hyp	Ref	Expression
1		idd 21	. . 3 |- ( ph -> ( ps -> ps ) )
2	1	a1i 9	. 2 |- (DECID ps -> ( ph -> ( ps -> ps ) ) )
3	2	impidc 788	1 |- (DECID ps -> ( -. ( ph -> -. ps ) -> ps ) )

Syntax hints:   -. wn 3   -> wi 4  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:  dfandc  811