alternatives
any no. two one none
any no. renders exh.
Γ ⊨ Σ
Γ, Σ ⊨ ⊥
  entails
Γ ⊨ ψ
(same)
inconsistent
Γ ⊨
Γ ⊨ ⊥
two       mutually excl.
φ, φ′ ⊨
φ, φ′ ⊨ ⊥
one     implies
φ ⊨ ψ
(same)
absurd
φ ⊨
φ ⊨ ⊥
none exhaustive
⊨ Σ
Σ ⊨ ⊥
jointly exh.
⊨ ψ, ψ′
ψ ⊨ ψ′
tautologous
⊨ ψ
(same)
 
 
  multiple alternatives positive
conclusion
negative:
no alternatives
  can replace alternatives
by assumptions
contradictory to them
  can replace
empty set
of alternatives
by conclusion ⊥