The universal quantifier may be dropped from a statement in a proof because of the
principle that any substitution instance whatsoever may be validly inferred from a
universally quantified proposition.

Question

The universal quantifier may be dropped from a statement in a proof because of the
 principle that any substitution instance whatsoever may be validly inferred from a
 universally quantified proposition.

Quizplus · Accepted Answer

The universal quantifier (denoted by ∀) indicates that the proposition holds for all elements in a particular domain. Therefore, any specific instance (substitution instance) derived from this universally quantified statement is considered valid, as it falls under the "all" category that the universal quantifier encompasses. This is why in proofs, it's often permissible to drop the universal quantifier when dealing with a specific instance, as the inference remains logically valid.

The Universal Quantifier May Be Dropped from a Statement in a Proof