Theorem 3mix2 1350

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 1349	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜒 ∨ 𝜓))
2		3orrot 1108	. 2 ⊢ ((𝜓 ∨ 𝜑 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓))
3	1, 2	sylibr 237	1 ⊢ (𝜑 → (𝜓 ∨ 𝜑 ∨ 𝜒))

This proof depends on syntax axioms:   → wi 4   ∨ w3o 1102

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862  df-3or 1104

This theorem is used by:  3mix2i  1353  3mix2d  1356  tppreqb  4764  tpres  7211  onzsl  7861  fnwe2lem4  8154  sornom  10362  nnz  12721  nn0le2is012  12770  hash1to3  14644  cshwshashlem1  17282  zabsle1  27632  ostth  27975  nolesgn2o  28037  nogesgn1o  28039  ltssolem1  28041  nosep1o  28047  nosep2o  28048  nodenselem8  28057  dfxlim2v  46965