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  4761  tpres  7147  onzsl  7788  sornom  10187  fpwwe2lem12  10553  nn0le2is012  12556  nn01to3  12854  qbtwnxr  13115  hash1to3  14415  swrdnd0  14581  pfxnd  14611  cshwshashlem1  17023  ostth  27606  nolesgn2o  27639  ltssolem1  27643  nosep2o  27650  btwncolinear1  36263  tpid3gVD  45092  limcicciooub  45891  dfxlim2v  46101