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Substitutions

For all terms S and T, formulas A and B, variables x and formula patterns C with variable F, the following holds:

Equality Subsitutions

S=T /\  A[x <- S]

A[x <- T]

Equivalence Substitutions

A <=> B /\  C[F <- A]

C[F <- B]

Replace "equal things by equal things", e.g., insert definitions.