Theorem orrd 367

Description: Deduce implication from disjunction. (Contributed by NM, 27-Nov-1995.)

Hypothesis

Ref	Expression
orrd.1	|- (ph -> (-. ps -> ch))

Assertion

Ref	Expression
orrd	|- (ph -> (ps \/ ch))

Proof of Theorem orrd

Step	Hyp	Ref	Expression
1		orrd.1	. 2 |- (ph -> (-. ps -> ch))
2		pm2.54 363	. 2 |- ((-. ps -> ch) -> (ps \/ ch))
3	1, 2	syl 15	1 |- (ph -> (ps \/ ch))

Syntax hints:  -. wn 3   -> wi 4   \/ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359

This theorem is referenced by:  olc  373  orc  374  pm2.68  399  pm4.79  566  sspss  3368  pwpw0  3855  sssn  3864  pwsnALT  3882  unissint  3950  pwadjoin  4119  nndisjeq  4429  xpexr  5109  fvclss  5462  erdisj  5972