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  4768  tpres  7201  onzsl  7843  sornom  10282  fpwwe2lem12  10654  nn0le2is012  12688  nn01to3  12993  qbtwnxr  13255  hash1to3  14560  swrdnd0  14730  pfxnd  14760  cshwshashlem1  17190  ostth  27878  nolesgn2o  27910  ltssolem1  27914  nosep2o  27921  btwncolinear1  36652  tpid3gVD  45667  limcicciooub  46468  dfxlim2v  46678