Definition:Semantic Equivalence/Predicate Logic/Definition 2

Definition

Let $\mathbf A, \mathbf B$ be WFFs of predicate logic.

Then $\mathbf A$ and $\mathbf B$ are equivalent if and only if:

$\mathbf A \iff \mathbf B$ is a tautology

where $\iff$ is the biconditional connective.

Also see

• Definition:Semantic Consequence (Predicate Logic)
• Definition:Logical Equivalence

Sources

• 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\mathrm{II}.8$ Further Semantic Notions: Definition $\mathrm{II.8.1}$