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  12464  fsum00  15771  pcfac  16877  mndifsplit  22530  bposlem2  27203  axcgrid  28850  3o2cs  32398  3o3cs  32399  fprodex01  32757  indsumin  32792  fsum2dsub  34605  finxpreclem2  37385  itg2addnclem  37672  tsan3  38144  xrninxpex  38387  disjimxrn  38748