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Theorem olcs 710
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 704 . 2 ((𝜓𝜑) → 𝜒)
32orcs 709 1 (𝜓𝜒)
Colors of variables: wff set class
Syntax hints:  wi 4  wo 682
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  equs5or  1786  sup3exmid  8683  0nn0  8960  xrlttri3  9551  fsum00  11199
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