Theorem 3mix1

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

	Ref	Expression
Assertion	3mix1	⊢ ( 𝜑 → ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		orc	⊢ ( 𝜑 → ( 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) )
2		3orass	⊢ ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) ↔ ( 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) )
3	1 2	sylibr	⊢ ( 𝜑 → ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) )