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  4756  tpres  7137  onzsl  7779  sornom  10171  fpwwe2lem12  10536  nn0le2is012  12540  nn01to3  12842  qbtwnxr  13102  hash1to3  14399  swrdnd0  14564  pfxnd  14594  cshwshashlem1  17007  ostth  27548  nolesgn2o  27581  sltsolem1  27585  nosep2o  27592  btwncolinear1  36047  tpid3gVD  44819  limcicciooub  45622  dfxlim2v  45832