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  4768  tpres  7205  onzsl  7855  sornom  10348  nnz  12707  nn0le2is012  12756  hash1to3  14630  cshwshashlem1  17266  zabsle1  27616  ostth  27959  nolesgn2o  28021  nogesgn1o  28023  ltssolem1  28025  nosep1o  28031  nosep2o  28032  nodenselem8  28041  fnwe2lem3  44038  dfxlim2v  46826