Description: Elimination of two disjuncts in a triple disjunction. (Contributed by Scott Fenton, 9-Jun-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | 3orel13 | ⊢ ( ( ¬ 𝜑 ∧ ¬ 𝜒 ) → ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) → 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3orel3 | ⊢ ( ¬ 𝜒 → ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) → ( 𝜑 ∨ 𝜓 ) ) ) | |
2 | orel1 | ⊢ ( ¬ 𝜑 → ( ( 𝜑 ∨ 𝜓 ) → 𝜓 ) ) | |
3 | 1 2 | sylan9r | ⊢ ( ( ¬ 𝜑 ∧ ¬ 𝜒 ) → ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) → 𝜓 ) ) |