Theorem olcs 654

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

Hypothesis

Ref	Expression
olcs.1	⊢ ((φ ∨ ψ) → χ)

Assertion

Ref	Expression
olcs	⊢ (ψ → χ)

Proof of Theorem olcs

Step	Hyp	Ref	Expression
1		olcs.1	. . 3 ⊢ ((φ ∨ ψ) → χ)
2	1	orcoms 648	. 2 ⊢ ((ψ ∨ φ) → χ)
3	2	orcs 653	1 ⊢ (ψ → χ)

Syntax hints:   → wi 4   ∨ wo 628

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  equs5or  1708  0nn0  7972  xrlttri3  8488