Theorem 3mix3 1328

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 1326	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒))
2		3orrot 1088	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑))
3	1, 2	sylib 220	1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ w3o 1082

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 209  df-or 844  df-3or 1084

This theorem is referenced by:  3mix3i  1331  3mix3d  1334  3jaob  1422  tppreqb  4740  tpres  6965  onzsl  7563  sornom  9701  fpwwe2lem13  10066  nn0le2is012  12049  nn01to3  12344  qbtwnxr  12596  hash1to3  13852  swrdnd0  14021  pfxnd  14051  cshwshashlem1  16431  ostth  26217  nolesgn2o  33180  sltsolem1  33182  btwncolinear1  33532  tpid3gVD  41183  limcicciooub  41925  dfxlim2v  42135