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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 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
olcs (𝜓𝜒)

Proof of Theorem olcs
StepHypRef Expression
1 olcs.1 . . 3 ((𝜑𝜓) → 𝜒)
21orcoms 872 . 2 ((𝜓𝜑) → 𝜒)
32orcs 875 1 (𝜓𝜒)
Colors of variables: wff setvar class
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  12543  fsum00  15835  pcfac  16938  mndifsplit  22643  bposlem2  27330  axcgrid  28932  3o2cs  32482  3o3cs  32483  fprodex01  32828  indsumin  32848  fsum2dsub  34623  finxpreclem2  37392  itg2addnclem  37679  tsan3  38151  ecexALTV  38333  cnvepimaex  38338  xrninxpex  38396  disjimxrn  38751
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