Metamath Proof Explorer


Theorem 3mix1

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

Ref Expression
Assertion 3mix1 ( 𝜑 → ( 𝜑𝜓𝜒 ) )

Proof

Step Hyp Ref Expression
1 orc ( 𝜑 → ( 𝜑 ∨ ( 𝜓𝜒 ) ) )
2 3orass ( ( 𝜑𝜓𝜒 ) ↔ ( 𝜑 ∨ ( 𝜓𝜒 ) ) )
3 1 2 sylibr ( 𝜑 → ( 𝜑𝜓𝜒 ) )