Theorem orcanai 929

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 725	. 2 |- ( ph -> ( -. ps -> ch ) )
3	2	imp 124	1 |- ( ( ph /\ -. ps ) -> ch )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104   \/ wo 709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in2 616  ax-io 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  fsumsplit  11572  pcgcd  12498  lgsdir2  15274