Theorem 3mix3d 1174

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

Hypothesis

Ref	Expression
3mixd.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
3mix3d	⊢ (𝜑 → (𝜒 ∨ 𝜃 ∨ 𝜓))

Proof of Theorem 3mix3d

Step	Hyp	Ref	Expression
1		3mixd.1	. 2 ⊢ (𝜑 → 𝜓)
2		3mix3 1168	. 2 ⊢ (𝜓 → (𝜒 ∨ 𝜃 ∨ 𝜓))
3	1, 2	syl 14	1 ⊢ (𝜑 → (𝜒 ∨ 𝜃 ∨ 𝜓))

Syntax hints:   → wi 4   ∨ w3o 977

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 709

This theorem depends on definitions:  df-bi 117  df-3or 979

This theorem is referenced by:  nnnegz  9229  prm23ge5  12231  zabsle1  13971  trirec0  14353