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We did not yet go through the trouble to interpret this (first order) ''difference of conjunction'' fully, but were happy simply to evaluate it with respect to a single location in the universe of discourse, namely, at the point picked out by the singular proposition ''xy'', in as much as if to say, at the place where ''x'' = 1 and ''y'' = 1.  This evaluation is written in the form ''Df''|''xy'' or ''Df''|<1, 1>, and we arrived at the locally applicable law that states that ''f'' = ''xy'' = ''x'' & ''y'' &rArr; ''Df''|''xy'' = ((''dx'')(''dy'')) = ''dx'' or ''dy''.

We did not yet go through the trouble to interpret this (first order) ''difference of conjunction'' fully, but were happy simply to evaluate it with respect to a single location in the universe of discourse, namely, at the point picked out by the singular proposition <math>xy,\!</math> in as much as if to say, at the place where <math>x = 1\!</math> and <math>y = 1.\!</math> This evaluation is written in the form <math>\operatorname{D}f|_{xy}</math> or <math>\operatorname{D}f|_{(1, 1)},</math> and we arrived at the locally applicable law that states that:

 

: <p><math>f = xy = x\ \operatorname{and}\ y \Rightarrow \operatorname{D}f|_{xy} = (\!|(\!| \operatorname{d}x |\!)(\!| \operatorname{d}y |\!)|\!) = \operatorname{d}x\ \operatorname{or}\ \operatorname{d}y.</math></p>

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