Theorem 3orel3 1485

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

Assertion

Ref	Expression
3orel3	⊢ (¬ 𝜒 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜓)))

Proof of Theorem 3orel3

Step	Hyp	Ref	Expression
1		df-3or 1087	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))
2		orel2 888	. 2 ⊢ (¬ 𝜒 → (((𝜑 ∨ 𝜓) ∨ 𝜒) → (𝜑 ∨ 𝜓)))
3	1, 2	syl5bi 241	1 ⊢ (¬ 𝜒 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜓)))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 844   ∨ w3o 1085

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-or 845  df-3or 1087

This theorem is referenced by:  ttrcltr  9474  3orel13  33660  nolesgn2o  33874  nosep2o  33885  noinfbnd1lem5  33930  noinfbnd2lem1  33933