Theorem 3mix2i 1353

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

Hypothesis

Ref	Expression
3mixi.1	⊢ 𝜑

Assertion

Ref	Expression
3mix2i	⊢ (𝜓 ∨ 𝜑 ∨ 𝜒)

Proof of Theorem 3mix2i

Step	Hyp	Ref	Expression
1		3mixi.1	. 2 ⊢ 𝜑
2		3mix2 1350	. 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒))
3	1, 2	ax-mp 5	1 ⊢ (𝜓 ∨ 𝜑 ∨ 𝜒)

This proof depends on syntax axioms:   ∨ w3o 1102

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862  df-3or 1104

This theorem is used by:  tpid2  4738  tpid2g  4739  ppiublem2  27418  nb3grprlem1  29788  gpgedgvtx0  48884  gpgedgvtx1  48885  gpgprismgr4cycllem3  48920  2zrngnring  49080