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  4756  tpres  7137  onzsl  7779  sornom  10171  nnz  12492  nn0le2is012  12540  hash1to3  14399  cshwshashlem1  17007  zabsle1  27205  ostth  27548  nolesgn2o  27581  nogesgn1o  27583  sltsolem1  27585  nosep1o  27591  nosep2o  27592  nodenselem8  27601  fnwe2lem3  43025  dfxlim2v  45828