Theorem 3orel13 1496

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

Assertion

Ref	Expression
3orel13	⊢ ((¬ 𝜑 ∧ ¬ 𝜒) → ((𝜑 ∨ 𝜓 ∨ 𝜒) → 𝜓))

Proof of Theorem 3orel13

Step	Hyp	Ref	Expression
1		3orel3 1495	. 2 ⊢ (¬ 𝜒 → ((𝜑 ∨ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜓)))
2		orel1 895	. 2 ⊢ (¬ 𝜑 → ((𝜑 ∨ 𝜓) → 𝜓))
3	1, 2	sylan9r 514	1 ⊢ ((¬ 𝜑 ∧ ¬ 𝜒) → ((𝜑 ∨ 𝜓 ∨ 𝜒) → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 397   ∨ wo 854   ∨ w3o 1092

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 209  df-an 398  df-or 855  df-3or 1094

This theorem is referenced by:  soseq  8103  nodenselem8  27677