Theorem sbidd-misc

Description: An identity theorem for substitution. See sbid . See Remark 9.1 in Megill p. 447 (p. 15 of the preprint). (Contributed by DAW, 18-Feb-2017)

	Ref	Expression
Assertion	sbidd-misc	$$⊢\left(\phi \to \left[x/x\right]\psi \right)\leftrightarrow \left(\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		sbid	$$⊢\left[x/x\right]\psi \leftrightarrow \psi$$
2	1	imbi2i	$$⊢\left(\phi \to \left[x/x\right]\psi \right)\leftrightarrow \left(\phi \to \psi \right)$$