Theorem orcanai 870

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 675	. 2 |- ( ph -> ( -. ps -> ch ) )
3	2	imp 122	1 |- ( ( ph /\ -. ps ) -> ch )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 102   \/ wo 661

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

This theorem is referenced by: (None)