Prop Logic Metatheorems

b/c they come up all the time:

Deduction Theorem: Δ |- (φ ⇒ ψ) if and only if
Δ∪{φ} |- ψ.

Substitution Theorem: Δ |- (φ ⇔ ψ) and Δ |- χ, then it
is the case that Δ |- χφ←ψ.

ChainingTheorem: IfΔ|-(φ⇒ψ)andΔ|-(ψ⇒χ), then Δ |- (φ ⇒ χ).

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