SheikhAndEmir

✱54·43: ⊦:.α,βε1.⊃:α∩β=Λ.≡.α∪βε2
 Dem.
  ⊦.✱54·26.⊃⊦:.α=℩'x.β=℩'y.⊃:α∪βε2.≡.x≠y.
  [✱51·231]           ≡.℩'x∩℩'y=Λ.
  [✱13·12]            ≡.α∩β=Λ   (1)
  ⊦.(1).✱11·11·35.⊃
   ⊦:.(∃x,y).α=℩'x.β=℩'y.⊃:α∪βε2.≡.α∩β=Λ   (2)
  ⊦.(2).✱11·54.✱52·1.⊃⊦.Prop
 From this proposition it will follow, when arithmetical addition has been
defined, that 1+1 = 2.