Theorem 3mix3 1334

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 1332	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒))
2		3orrot 1092	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑))
3	1, 2	sylib 218	1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ w3o 1086

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 849  df-3or 1088

This theorem is referenced by:  3mix3i  1337  3mix3d  1340  3jaobOLD  1430  tppreqb  4749  tpres  7150  onzsl  7791  sornom  10193  fpwwe2lem12  10559  nn0le2is012  12587  nn01to3  12885  qbtwnxr  13146  hash1to3  14448  swrdnd0  14614  pfxnd  14644  cshwshashlem1  17060  ostth  27619  nolesgn2o  27652  ltssolem1  27656  nosep2o  27663  btwncolinear1  36270  tpid3gVD  45289  limcicciooub  46086  dfxlim2v  46296