Theorem olcs 726

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 720	. 2 |- ( ( ps \/ ph ) -> ch )
3	2	orcs 725	1 |- ( ps -> ch )

Syntax hints:   -> wi 4   \/ wo 698

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-io 699

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  equs5or  1818  sup3exmid  8852  0nn0  9129  xrlttri3  9733  fsum00  11403  pcfac  12280