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  4769  tpres  7175  onzsl  7822  sornom  10230  fpwwe2lem12  10595  nn0le2is012  12598  nn01to3  12900  qbtwnxr  13160  hash1to3  14457  swrdnd0  14622  pfxnd  14652  cshwshashlem1  17066  ostth  27550  nolesgn2o  27583  sltsolem1  27587  nosep2o  27594  btwncolinear1  36057  tpid3gVD  44831  limcicciooub  45635  dfxlim2v  45845