Theorem pm2.25dc 792

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 743	. 2 |- (DECID ph <-> ( ph \/ -. ph ) )
2		orel1 644	. . 3 |- ( -. ph -> ( ( ph \/ ps ) -> ps ) )
3	2	orim2i 678	. 2 |- ( ( ph \/ -. ph ) -> ( ph \/ ( ( ph \/ ps ) -> ps ) ) )
4	1, 3	sylbi 114	1 |- (DECID ph -> ( ph \/ ( ( ph \/ ps ) -> ps ) ) )

Syntax hints:   -. wn 3   -> wi 4   \/ wo 629  DECID wdc 742

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110  df-dc 743

This theorem is referenced by: (None)