Theorem orcs 730

Description: Deduction eliminating disjunct. Notational convention: We sometimes suffix with "s" the label of an inference that manipulates an antecedent, leaving the consequent unchanged. The "s" means that the inference eliminates the need for a syllogism (syl 14) -type inference in a proof. (Contributed by NM, 21-Jun-1994.)

Hypothesis

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

Assertion

Ref	Expression
orcs	|- ( ph -> ch )

Proof of Theorem orcs

Step	Hyp	Ref	Expression
1		orc 707	. 2 |- ( ph -> ( ph \/ ps ) )
2		orcs.1	. 2 |- ( ( ph \/ ps ) -> ch )
3	1, 2	syl 14	1 |- ( ph -> ch )

Syntax hints:   -> wi 4   \/ wo 703

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-io 704

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  olcs  731  ifordc  3564  sqxpeq0  5034