Theorem 3mix1d

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

	Ref	Expression
Hypothesis	3mixd.1	⊢ ( 𝜑 → 𝜓 )
Assertion	3mix1d	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ∨ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		3mixd.1	⊢ ( 𝜑 → 𝜓 )
2		3mix1	⊢ ( 𝜓 → ( 𝜓 ∨ 𝜒 ∨ 𝜃 ) )
3	1 2	syl	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ∨ 𝜃 ) )