Theorem orcs 383

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 15) -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 374	. 2 |- (ph -> (ph \/ ps))
2		orcs.1	. 2 |- ((ph \/ ps) -> ch)
3	1, 2	syl 15	1 |- (ph -> ch)

This proof depends on syntax axioms:   -> wi 4   \/ wo 357

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-or 359

This theorem is used by:  olcs  384  ifor  3703