And analogously: not “(∃x, y).f(x, y).x = y”, but “(∃x).f(x, x)”; and not “(∃x, y) . f(x, y) . ∼x = y”, but “(∃x, y) . f(x, y)”. (Therefore instead of Russell’s “(∃x, y) . f(x, y)”: “(∃x, y) . f(x, y) . ∨ . (∃x) . f(x, x)”.) 5.5321 Instead of “(x) : fx ⊃ x = a” we therefore write e.g. “(∃x).fx. ⊃ .fa : ∼(∃x, y) . fx . fy”. And the proposition “only one x satisfies f()” reads: “(∃x) . fx : ∼(∃x, y) . fx . fy”.
