Theorem olcs 748

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 742	. 2 ⊢ ((𝜓 ∨ 𝜑) → 𝜒)
3	2	orcs 747	1 ⊢ (𝜓 → 𝜒)

This proof depends on syntax axioms:   → wi 4   ∨ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  equs5or  1883  sup3exmid  9290  0nn0  9583  xrlttri3  10210  flaplt  10733  fsum00  12248  pcfac  13152  bposlem2  16278