
Universal Instantiation:
x P(x)

P(c)
where c is some arbitrary element of the universe.
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Universal Instantiation
for further explanations and examples.

Universal Generalization:
P(c)

x P(x)
where P(c) holds for every element c of the universe of discourse.
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Universal Generalization
for further explanations and examples.

Existential Instantiation:
x P(x)

P(c)
where c is some element of the universe of discourse. It is not arbitrary but must be one for which P(c) is true.
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Existential Instantiation
for further explanations and examples.

Existential Generalization:
P(c)

x P(x)
where c is an element of the universe.
Go to
Existential Generalization
for further explanations and examples.