P1 wxyz((w ex Y & x ex Y)(w ex Zx ex Z))

(Individuals that co-exemplify any haecceity exemplify the same haecceities.)

P2 xy(x = yz(x ex Z & y ex Z))

(Individuals are identical if they co-exemplify some haecceity.)

P3 xy(x ex Yy ex Y)

(If x exemplifies Y, y exemplifies Y.)

P4 wxyz(y ex W & y ex X(z ex W z ex X))

(Haecceities co-exemplified by any individual are exemplified by the same individuals.)

P5 xy(X = Yz(z ex X & z ex Y))

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(Haecceities are identical if they are co-exemplified by some individual.)

P6 xy(x ex Yx ex X)

(If x exemplifies Y, x exemplifies X.)