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  10280  fpwwe2lem12  10652  nn0le2is012  12686  nn01to3  12991  qbtwnxr  13253  hash1to3  14558  swrdnd0  14728  pfxnd  14758  cshwshashlem1  17188  ostth  27876  nolesgn2o  27908  ltssolem1  27912  nosep2o  27919  btwncolinear1  36650  tpid3gVD  45665  limcicciooub  46466  dfxlim2v  46676