Theorem 3mix3i 1166

Description: Introduction in triple disjunction. (Contributed by Mario Carneiro, 6-Oct-2014.)

Hypothesis

Ref	Expression
3mixi.1	⊢ 𝜑

Assertion

Ref	Expression
3mix3i	⊢ (𝜓 ∨ 𝜒 ∨ 𝜑)

Proof of Theorem 3mix3i

Step	Hyp	Ref	Expression
1		3mixi.1	. 2 ⊢ 𝜑
2		3mix3 1163	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ∨ 𝜒 ∨ 𝜑)

Syntax hints:   ∨ w3o 972

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704

This theorem depends on definitions:  df-bi 116  df-3or 974

This theorem is referenced by:  tpid3  3699