substitution

mathematics and logic

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July 14, 2026

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Substitution, in mathematics and logic, is the act of replacing one entity with another of equal value. This process is fundamental in areas like combinatory logic, which specifically deals with substitution and the elimination of variables.12

In the context of algebraic equations, substitution is the method used to solve them. When a number or set of numbers is substituted for the variables in an equation, it should reduce the equation to an identity, meaning both sides are equal. A statement derived from a statement form by substituting constants for variables is known as a substitution instance in logic.34

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formal logic
Axiomatization of PC
…axiom”; analogous schemata can be substituted for the other axioms. The number of axioms would then become infinite, but, on the other hand, the rule of substitution would no longer be needed, and modus ponens could be the only transformation rule. This method makes no difference to the theorems that…
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…axiom”; analogous schemata can be substituted for the other axioms. The number of axioms would then become infinite, but, on the other hand, the rule of substitution would no longer be needed, and modus ponens could be the only transformation rule. This method makes no difference to the theorems that…
Read More