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Equality

Predicate constant with the following properties, for all x, y, and z:

• Reflexivity: x = x;
• Symmetry: x = y => y = x;
• Transitivity: (x = y /\  y = z) => x=z.

• Equality Axiom (every function constant f or predicate constant p)

  x = y	=>	f(..., x, ...) = f(..., y, ...);
  x = y	=>	p(..., x, ...) <=> p(..., y, ...).

First Order Predicate Logic with Equality.