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  4759  tpres  7145  onzsl  7786  sornom  10185  nnz  12507  nn0le2is012  12554  hash1to3  14413  cshwshashlem1  17021  zabsle1  27261  ostth  27604  nolesgn2o  27637  nogesgn1o  27639  sltsolem1  27641  nosep1o  27647  nosep2o  27648  nodenselem8  27657  fnwe2lem3  43236  dfxlim2v  46033