Such a replacement can be viewed as a rule of inference.

We know that humans do not reason entirely from facts, using consistent rules of inference.

There are several rules of inference which utilize the universal quantifier.

Typically, a rule of inference preserves truth, a semantic property.

It is very closely related to the rule of inference modus tollens.

Another view is that people rely on domain-specific or content-sensitive rules of inference.

Rules of inference must be distinguished from axioms of a theory.

As before, all rules of inference in finitary logic can be used, together with an additional one:

The substitution rule demonstrates several common aspects of rules of inference.

In other formal proof systems, the deduction theorem is sometimes taken as a primitive rule of inference.

For example, one common rule of inference is the rule of substitution.

Simplification is a rule of inference in logic.

Q has a single rule of inference.

An example of this is the use of the rules of inference found within symbolic logic.

The primitive rules of inference are the following:

See List of rules of inference for examples.

Modus ponens is a very common rule of inference, and takes the following form:

First-order logic requires at least one additional rule of inference in order to obtain completeness.

The rule of inference for necessary condition is modus tollens:

It is common to have only modus ponens and universal generalization as rules of inference.

In propositional logic, biconditional introduction is a valid rule of inference.

A rule of inference is a rule justifying a logical step from hypothesis to conclusion.

The goal was to find valid rules of inference and forms of proof to help people find their way in life.

The rules of inference enable the manipulation of quantifiers.

I understand you to likewise believe that [X] and to endorse these same rules of inference.