View source for Minimal functional calculus

''minimal predicate calculus''

The calculus of predicates given by all axiom schemes of the [[Minimal propositional calculus|minimal propositional calculus]] and by the usual quantifier axiom schemes and deduction rules, that is,

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m063/m063820/m0638201.png" /></td> </tr></table>

(<img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m063/m063820/m0638202.png" /> an arbitrary term), [[Modus ponens|modus ponens]] and

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(provided the variable <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m063/m063820/m0638204.png" /> does not occur in <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m063/m063820/m0638205.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/m/m063/m063820/m0638206.png" />).

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  A. Church,   "Introduction to mathematical logic" , '''1''' , Princeton Univ. Press  (1956)</TD></TR></table>