Theorem 3mix3d

Description: Deduction introducing triple disjunction. (Contributed by Scott Fenton, 8-Jun-2011)

	Ref	Expression
Hypothesis	3mixd.1	$$⊢\phi \to \psi$$
Assertion	3mix3d	$$⊢\phi \to \left(\chi \vee \theta \vee \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		3mixd.1	$$⊢\phi \to \psi$$
2		3mix3	$$⊢\psi \to \left(\chi \vee \theta \vee \psi \right)$$
3	1 2	syl	$$⊢\phi \to \left(\chi \vee \theta \vee \psi \right)$$