Theorem pm4.67dc 872

Description: Theorem *4.67 of [WhiteheadRussell] p. 120, for decidable propositions. (Contributed by Jim Kingdon, 1-May-2018.)

Assertion

Ref	Expression
pm4.67dc	|- (DECID ph -> (DECID ps -> ( -. ( -. ph -> -. ps ) <-> ( -. ph /\ ps ) ) ) )

Proof of Theorem pm4.67dc

Step	Hyp	Ref	Expression
1		dcn 827	. 2 |- (DECID ph -> DECID -. ph )
2		pm4.63dc 871	. 2 |- (DECID -. ph -> (DECID ps -> ( -. ( -. ph -> -. ps ) <-> ( -. ph /\ ps ) ) ) )
3	1, 2	syl 14	1 |- (DECID ph -> (DECID ps -> ( -. ( -. ph -> -. ps ) <-> ( -. ph /\ ps ) ) ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 103   <-> wb 104  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-stab 816  df-dc 820

This theorem is referenced by: (None)