Theorem dfor2dc 907

Description: Disjunction expressed in terms of implication only, for a decidable proposition. Based on theorem *5.25 of [WhiteheadRussell] p. 124. (Contributed by Jim Kingdon, 27-Mar-2018.)

Assertion

Ref	Expression
dfor2dc	|- (DECID ph -> ( ( ph \/ ps ) <-> ( ( ph -> ps ) -> ps ) ) )

Proof of Theorem dfor2dc

Step	Hyp	Ref	Expression
1		pm2.62 760	. 2 |- ( ( ph \/ ps ) -> ( ( ph -> ps ) -> ps ) )
2		pm2.68dc 906	. 2 |- (DECID ph -> ( ( ( ph -> ps ) -> ps ) -> ( ph \/ ps ) ) )
3	1, 2	impbid2 143	1 |- (DECID ph -> ( ( ph \/ ps ) <-> ( ( ph -> ps ) -> ps ) ) )

This proof depends on syntax axioms:   -> wi 4   <-> wb 105   \/ wo 720  DECID wdc 846

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624  ax-io 721

This proof depends on definitions:  df-bi 117  df-dc 847

This theorem is used by:  imimorbdc  908