Theorem 3orel1 1106

Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011.)

Assertion

Ref	Expression
3orel1	⊢ (¬ 𝜑 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜓 ∨ 𝜒)))

Proof of Theorem 3orel1

Step	Hyp	Ref	Expression
1		3orass 1105	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
2		orel1 901	. 2 ⊢ (¬ 𝜑 → ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ 𝜒)))
3	1, 2	biimtrid 245	1 ⊢ (¬ 𝜑 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜓 ∨ 𝜒)))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 860   ∨ w3o 1101

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 861  df-3or 1103

This theorem is used by:  3orel2  1514  3orel2OLD  1515