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Metamath Proof Explorer

Theorem 3mix3i

Description: Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014)

Ref Expression
Hypothesis 3mixi.1 ⊢ 𝜑
Assertion 3mix3i ( 𝜓 ∨ 𝜒 ∨ 𝜑 )

Proof

Step Hyp Ref Expression
1 3mixi.1 ⊢ 𝜑
2 3mix3 ⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ∨ 𝜑 ) )
3 1 2 ax-mp ⊢ ( 𝜓 ∨ 𝜒 ∨ 𝜑 )