Theorem sbidd

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
Hypothesis	sbidd.1	$$⊢\phi \to \left[x/x\right]\psi$$
Assertion	sbidd	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		sbidd.1	$$⊢\phi \to \left[x/x\right]\psi$$
2		sbid	$$⊢\left[x/x\right]\psi \leftrightarrow \psi$$
3	1 2	sylib	$$⊢\phi \to \psi$$