Theorem 3mix2 1333

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 1332	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒 ∨ 𝜓))
2		3orrot 1092	. 2 ⊢ ((𝜓 ∨ 𝜑 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓))
3	1, 2	sylibr 234	1 ⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒))

Syntax hints:   → wi 4   ∨ w3o 1086

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 849  df-3or 1088

This theorem is referenced by:  3mix2i  1336  3mix2d  1339  3jaobOLD  1430  tppreqb  4750  tpres  7156  onzsl  7797  sornom  10199  nnz  12545  nn0le2is012  12593  hash1to3  14454  cshwshashlem1  17066  zabsle1  27259  ostth  27602  nolesgn2o  27635  nogesgn1o  27637  ltssolem1  27639  nosep1o  27645  nosep2o  27646  nodenselem8  27655  fnwe2lem3  43480  dfxlim2v  46275