Theorem olcs 410

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 404	. 2 ⊢ ((𝜓 ∨ 𝜑) → 𝜒)
3	2	orcs 409	1 ⊢ (𝜓 → 𝜒)

Syntax hints:   → wi 4   ∨ wo 383

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 197  df-or 385

This theorem is referenced by:  0nn0  11307  fsum00  14530  pcfac  15603  mndifsplit  20442  bposlem2  25010  axcgrid  25796  3o2cs  29310  3o3cs  29311  fprodex01  29571  indsumin  30084  fsum2dsub  30685  finxpreclem2  33227  itg2addnclem  33461  tsan3  33950