Theorem 3mix1

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

	Ref	Expression
Assertion	3mix1	$$⊢\phi \to \left(\phi \vee \psi \vee \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		orc	$$⊢\phi \to \left(\phi \vee \left(\psi \vee \chi \right)\right)$$
2		3orass	$$⊢\left(\phi \vee \psi \vee \chi \right)\leftrightarrow \left(\phi \vee \left(\psi \vee \chi \right)\right)$$
3	1 2	sylibr	$$⊢\phi \to \left(\phi \vee \psi \vee \chi \right)$$