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Notes for Abstract
1. (1)-(3) are theorems in the minimal system P.
(1) for allxfor ally(x = y if-then (y = x))

(2) for allxfor allyfor allz((x = y & y = z) if-then (x = z))

(3) for allxfor allyfor allz(x = y if-then ((x emb Z) equivalent (y emb Z))

(4) figures as a theorem in P+, the classical extension of P.
(4) for allx(x = x)
2. See 'The Paradox of Identity'.

3. See 'Let X = X But Not Necessarily'. 

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