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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 648 | . 2 ⊢ ((ψ ∨ φ) → χ) |
3 | 2 | orcs 653 | 1 ⊢ (ψ → χ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 628 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 629 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: equs5or 1708 0nn0 7972 xrlttri3 8488 |
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