Theorem orcanai 837

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 643	. 2 |- ( ph -> ( -. ps -> ch ) )
3	2	imp 115	1 |- ( ( ph /\ -. ps ) -> ch )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 97   \/ wo 629

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

This theorem is referenced by: (None)