Theorem orcanai 923

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 719	. 2 |- ( ph -> ( -. ps -> ch ) )
3	2	imp 123	1 |- ( ( ph /\ -. ps ) -> ch )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 103   \/ wo 703

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 610  ax-io 704

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  fsumsplit  11370  pcgcd  12282  lgsdir2  13728