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  4770  tpres  7238  onzsl  7891  fnwe2lem4  8185  sornom  10394  nnz  12754  nn0le2is012  12803  hash1to3  14678  cshwshashlem1  17317  zabsle1  27680  ostth  28023  nolesgn2o  28085  nogesgn1o  28087  ltssolem1  28089  nosep1o  28095  nosep2o  28096  nodenselem8  28105  dfxlim2v  47130