Substitution of Equivalents | Logic I

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Substitution of Equivalents

Suppose that φ, ψ and χ are sentences of awFOL. Suppose that φ is logically equivalent to ψ. Let χ[φ/ψ] be the result of replacing, in χ, zero or more occurrences of φ with ψ. The \emph{subsitution theorem} says that χ[φ/ψ] is logically equivalent to χ.

A ∧ B ⫤⊨ ¬(¬A ∨ ¬B)

A ∨ B ⫤⊨ ¬(¬A ∧ ¬B)

A → B ⫤⊨ ¬A ∨ B

¬¬(¬A ∧ ¬B) ⫤⊨ ¬(A ∨ B)

7.25

4.31, 7.25