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  4763  tpres  7157  onzsl  7798  sornom  10199  fpwwe2lem12  10565  nn0le2is012  12568  nn01to3  12866  qbtwnxr  13127  hash1to3  14427  swrdnd0  14593  pfxnd  14623  cshwshashlem1  17035  ostth  27618  nolesgn2o  27651  ltssolem1  27655  nosep2o  27662  btwncolinear1  36285  tpid3gVD  45197  limcicciooub  45995  dfxlim2v  46205