Theorem 3mix2 1332

Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Assertion

Ref	Expression
3mix2	⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒))

Proof of Theorem 3mix2

Step	Hyp	Ref	Expression
1		3mix1 1331	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒 ∨ 𝜓))
2		3orrot 1091	. 2 ⊢ ((𝜓 ∨ 𝜑 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓))
3	1, 2	sylibr 234	1 ⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒))

Syntax hints:   → wi 4   ∨ w3o 1085

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-or 848  df-3or 1087

This theorem is referenced by:  3mix2i  1335  3mix2d  1338  3jaobOLD  1429  tppreqb  4769  tpres  7175  onzsl  7822  sornom  10230  nnz  12550  nn0le2is012  12598  hash1to3  14457  cshwshashlem1  17066  zabsle1  27207  ostth  27550  nolesgn2o  27583  nogesgn1o  27585  sltsolem1  27587  nosep1o  27593  nosep2o  27594  nodenselem8  27603  fnwe2lem3  43041  dfxlim2v  45845