Theorem 3mix1d 1174

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

Hypothesis

Ref	Expression
3mixd.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
3mix1d	⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜃))

Proof of Theorem 3mix1d

Step	Hyp	Ref	Expression
1		3mixd.1	. 2 ⊢ (𝜑 → 𝜓)
2		3mix1 1168	. 2 ⊢ (𝜓 → (𝜓 ∨ 𝜒 ∨ 𝜃))
3	1, 2	syl 14	1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜃))

Syntax hints:   → wi 4   ∨ w3o 979

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117  df-3or 981

This theorem is referenced by:  trirec0  15688