Theorem olcs 876

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 872	. 2 ⊢ ((𝜓 ∨ 𝜑) → 𝜒)
3	2	orcs 875	1 ⊢ (𝜓 → 𝜒)

Syntax hints:   → wi 4   ∨ wo 847

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-or 848

This theorem is referenced by:  0nn0  12416  fsum00  15721  pcfac  16827  mndifsplit  22580  bposlem2  27252  axcgrid  28989  3o2cs  32536  3o3cs  32537  fprodex01  32906  indsumin  32943  fsum2dsub  34764  finxpreclem2  37591  itg2addnclem  37868  tsan3  38340  xrninxpex  38598  disjimxrn  39004