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 any 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)) 
(Haecceities are identical if any individual co-exemplifies them.) 

P6 xy(x ex Yx ex X) 
(If x exemplifies Y, x exemplifies X.)

P7 wxyz(w.X = y.Z(w ex X & w ex Z & y ex X)) 
(w.X = y.Z if w exemplifies X and Z, and y exemplifies X.) 

P8 xyz(x.Y emb Zx ex Y & x ex Z) 
(x.Y embodies Z if x exemplifies Y and Z.)

P9 xyz(x.Y cont zx ex Y & z ex Y) 
(x.Y contains z if x and z exemplify Y.) 

I1: From  to infer , where  results from  by substituting t for t.T at one or more places of its occurrence.

I2: From  to infer , where  results from  by substituting  t.T for t at one or more places of its occurrence.