Theorem 3mix3 1351

Description: Introduction in triple disjunction. (Contributed by NM, 4-Apr-1995.)

Assertion

Ref	Expression
3mix3	⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑))

Proof of Theorem 3mix3

Step	Hyp	Ref	Expression
1		3mix1 1349	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒))
2		3orrot 1108	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑))
3	1, 2	sylib 221	1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑))

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:  3mix3i  1354  3mix3d  1357  tppreqb  4764  tpres  7211  onzsl  7861  sornom  10362  fpwwe2lem12  10734  nn0le2is012  12770  nn01to3  13075  qbtwnxr  13337  hash1to3  14644  swrdnd0  14815  pfxnd  14845  cshwshashlem1  17282  ostth  27975  nolesgn2o  28037  ltssolem1  28041  nosep2o  28048  btwncolinear1  36958  tpid3gVD  45960  limcicciooub  46783  dfxlim2v  46993