Theorem pm2.25dc 825

Description: Elimination of disjunction based on a disjunction, for a decidable proposition. Based on theorem *2.25 of [WhiteheadRussell] p. 104. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.25dc	|- (DECID ph -> ( ph \/ ( ( ph \/ ps ) -> ps ) ) )

Proof of Theorem pm2.25dc

Step	Hyp	Ref	Expression
1		df-dc 776	. 2 |- (DECID ph <-> ( ph \/ -. ph ) )
2		orel1 676	. . 3 |- ( -. ph -> ( ( ph \/ ps ) -> ps ) )
3	2	orim2i 710	. 2 |- ( ( ph \/ -. ph ) -> ( ph \/ ( ( ph \/ ps ) -> ps ) ) )
4	1, 3	sylbi 119	1 |- (DECID ph -> ( ph \/ ( ( ph \/ ps ) -> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 661  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-in2 577  ax-io 662

This theorem depends on definitions:  df-bi 115  df-dc 776

This theorem is referenced by: (None)