Theorem 3mix3 1333

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 1331	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒))
2		3orrot 1091	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑))
3	1, 2	sylib 218	1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ w3o 1085

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 848  df-3or 1087

This theorem is referenced by:  3mix3i  1336  3mix3d  1339  3jaobOLD  1429  tppreqb  4759  tpres  7145  onzsl  7786  sornom  10185  fpwwe2lem12  10551  nn0le2is012  12554  nn01to3  12852  qbtwnxr  13113  hash1to3  14413  swrdnd0  14579  pfxnd  14609  cshwshashlem1  17021  ostth  27604  nolesgn2o  27637  sltsolem1  27641  nosep2o  27648  btwncolinear1  36212  tpid3gVD  45024  limcicciooub  45823  dfxlim2v  46033