Metamath Proof Explorer


Theorem 3orel13

Description: Elimination of two disjuncts in a triple disjunction. (Contributed by Scott Fenton, 9-Jun-2011)

Ref Expression
Assertion 3orel13 ( ( ¬ 𝜑 ∧ ¬ 𝜒 ) → ( ( 𝜑𝜓𝜒 ) → 𝜓 ) )

Proof

Step Hyp Ref Expression
1 3orel3 ( ¬ 𝜒 → ( ( 𝜑𝜓𝜒 ) → ( 𝜑𝜓 ) ) )
2 orel1 ( ¬ 𝜑 → ( ( 𝜑𝜓 ) → 𝜓 ) )
3 1 2 sylan9r ( ( ¬ 𝜑 ∧ ¬ 𝜒 ) → ( ( 𝜑𝜓𝜒 ) → 𝜓 ) )