Theorem olcs 687

Description: Deduction eliminating disjunct. (Contributed by NM, 21-Jun-1994.) (Proof shortened by Wolf Lammen, 3-Oct-2013.)

Hypothesis

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

Assertion

Ref	Expression
olcs	|- ( ps -> ch )

Proof of Theorem olcs

Step	Hyp	Ref	Expression
1		olcs.1	. . 3 |- ( ( ph \/ ps ) -> ch )
2	1	orcoms 681	. 2 |- ( ( ps \/ ph ) -> ch )
3	2	orcs 686	1 |- ( ps -> ch )

Syntax hints:   -> wi 4   \/ 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-io 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  equs5or  1751  0nn0  8303  xrlttri3  8872