Theorem orcanai 879

Description: Change disjunction in consequent to conjunction in antecedent. (Contributed by NM, 8-Jun-1994.)

Hypothesis

Ref	Expression
orcanai.1	|- (ph -> (ps \/ ch))

Assertion

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

Proof of Theorem orcanai

Step	Hyp	Ref	Expression
1		orcanai.1	. . 3 |- (ph -> (ps \/ ch))
2	1	ord 366	. 2 |- (ph -> (-. ps -> ch))
3	2	imp 418	1 |- ((ph /\ -. ps) -> ch)

Syntax hints:  -. wn 3   -> wi 4   \/ wo 357   /\ wa 358

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  df-an 360

This theorem is referenced by: (None)