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  4749  tpres  7149  onzsl  7790  sornom  10190  nnz  12536  nn0le2is012  12584  hash1to3  14445  cshwshashlem1  17057  zabsle1  27273  ostth  27616  nolesgn2o  27649  nogesgn1o  27651  ltssolem1  27653  nosep1o  27659  nosep2o  27660  nodenselem8  27669  fnwe2lem3  43498  dfxlim2v  46293