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And analogously: not "( EXISTS x,y) . f(x,y) . x=y", but "( EXISTS x) . f(x,x)" and not "( EXISTS x,y) . f(x,y) . ~ x=y", but "( EXISTS x,y) . f(x,y)".

(Therefore instead of Russell's "( EXISTS x,y) . f(x,y)",

"( EXISTS x,y) . f(x,y) . v .( EXISTS x) . f(x,x)". )

5.5321    Instead of "(x) : Fx  HOOK  x = a" we therefore write e.g. "( EXISTS x). fx .  HOOK  . fa : ~( EXISTS x,y) . fx . fy".

And the proposition "only one x satisfies f()" reads: "( EXISTS x). fx : ~( EXISTS x,y) . fx . fy".