Theorem 3orel3 1516

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 1103	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))
2		orel2 903	. 2 ⊢ (¬ 𝜒 → (((𝜑 ∨ 𝜓) ∨ 𝜒) → (𝜑 ∨ 𝜓)))
3	1, 2	biimtrid 245	1 ⊢ (¬ 𝜒 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜓)))

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:  3orel13  1517  ttrcltr  9683  nolesgn2o  27846  nosep2o  27857  noinfbnd1lem5  27902  noinfbnd2lem1  27905