something is identical with Pegasus. The problem comes from substituting nondesignating constants for variables: in fact, we cannot do this in standard formulations of first-order logic, since there are no nondesignating constants. Classically, ?x(x=y) is deducible from the open equality axiom y=y by particularization (i.e. (3) above).

In free logic, (1) is replaced with

:1b. , where E! is an existence predicate (in some but not all formulations of free logic, E!t can be defined as

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