Theorem olcs 731

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 725	. 2 ⊢ ((𝜓 ∨ 𝜑) → 𝜒)
3	2	orcs 730	1 ⊢ (𝜓 → 𝜒)

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-ia2 106  ax-ia3 107  ax-io 704

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  equs5or  1823  sup3exmid  8873  0nn0  9150  xrlttri3  9754  fsum00  11425  pcfac  12302