Theorem dfor2dc 890

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		pm2.62 743	. 2 |- ( ( ph \/ ps ) -> ( ( ph -> ps ) -> ps ) )
2		pm2.68dc 889	. 2 |- (DECID ph -> ( ( ( ph -> ps ) -> ps ) -> ( ph \/ ps ) ) )
3	1, 2	impbid2 142	1 |- (DECID ph -> ( ( ph \/ ps ) <-> ( ( ph -> ps ) -> ps ) ) )

Syntax hints:   -> wi 4   <-> wb 104   \/ wo 703  DECID wdc 829

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 609  ax-in2 610  ax-io 704

This theorem depends on definitions:  df-bi 116  df-dc 830

This theorem is referenced by:  imimorbdc  891