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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 681 | . 2 ⊢ ((𝜓 ∨ 𝜑) → 𝜒) |
3 | 2 | orcs 686 | 1 ⊢ (𝜓 → 𝜒) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 661 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: equs5or 1751 0nn0 8303 xrlttri3 8872 |
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