Theorem 3mix3 1351

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 1349	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒))
2		3orrot 1108	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑))
3	1, 2	sylib 221	1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑))

This proof depends on syntax axioms:   → wi 4   ∨ w3o 1102

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862  df-3or 1104

This theorem is used by:  3mix3i  1354  3mix3d  1357  tppreqb  4770  tpres  7238  onzsl  7891  sornom  10394  fpwwe2lem12  10766  nn0le2is012  12803  nn01to3  13108  qbtwnxr  13370  hash1to3  14678  swrdnd0  14849  pfxnd  14879  cshwshashlem1  17317  ostth  28023  nolesgn2o  28085  ltssolem1  28089  nosep2o  28096  btwncolinear1  37049  tpid3gVD  46084  limcicciooub  46920  dfxlim2v  47130