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Mirrors > Home > ILE Home > Th. List > olcs | GIF version |
Description: Deduction eliminating disjunct. (Contributed by NM, 21-Jun-1994.) (Proof shortened by Wolf Lammen, 3-Oct-2013.) |
Ref | Expression |
---|---|
olcs.1 | ⊢ ((𝜑 ∨ 𝜓) → 𝜒) |
Ref | Expression |
---|---|
olcs | ⊢ (𝜓 → 𝜒) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | olcs.1 | . . 3 ⊢ ((𝜑 ∨ 𝜓) → 𝜒) | |
2 | 1 | orcoms 725 | . 2 ⊢ ((𝜓 ∨ 𝜑) → 𝜒) |
3 | 2 | orcs 730 | 1 ⊢ (𝜓 → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 703 |
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 704 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: equs5or 1823 sup3exmid 8866 0nn0 9143 xrlttri3 9747 fsum00 11418 pcfac 12295 |
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