Metamath Proof Explorer


Theorem 3mix3

Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995)

Ref Expression
Assertion 3mix3 ( 𝜑 → ( 𝜓 ∨ 𝜒 ∨ 𝜑 ) )

Proof

Step Hyp Ref Expression
1 3mix1 ⊢ ( 𝜑 → ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) )
2 3orrot ⊢ ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) ↔ ( 𝜓 ∨ 𝜒 ∨ 𝜑 ) )
3 1 2 sylib ⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ∨ 𝜑 ) )