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(here I use "A" for the universal quantifier, "E" for the existential quantifier, and "e" to indicate elementhood)

My present definition for Transitivity of a relation:

R is a transitive relation on the set B

AxeB AyeB AzeB [((x,y)eR & (y,z)eR)-->(x,z)eR]

which I shorten to:

Ax,y,zeB[((x,y)eR & (y,z)eR)-->(x,z)eR]

But for a certain proof I need Ey rather than Ay, so I'm wondering if I can use a 3-tuple, (x,y,z), in the following way:

A(x,y,z)eB[((x,y)eR & (y,z)eR)-->(x,z)eR]

or would that mean I'd have to be using B^3??

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# Correct use of 3-tuple ?

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