Theorem 3mix3 1168

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 1166	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓 ∨ 𝜒))
2		3orrot 984	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜓 ∨ 𝜒 ∨ 𝜑))
3	1, 2	sylib 122	1 ⊢ (𝜑 → (𝜓 ∨ 𝜒 ∨ 𝜑))

Syntax hints:   → wi 4   ∨ w3o 977

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709

This theorem depends on definitions:  df-bi 117  df-3or 979

This theorem is referenced by:  3mix3i  1171  3mix3d  1174  3jaob  1302  tpid3g  3707  funtpg  5265  exmidontriimlem3  7218  nn0le2is012  9330  nn01to3  9612  fztri3or  10033  qbtwnxr  10252  hashfiv01gt1  10754