Theorem sbid2vw

Description: Reverting substitution yields the original expression. Based on fewer axioms than sbid2v , at the expense of an extra distinct variable condition. (Contributed by NM, 14-May-1993) (Revised by Wolf Lammen, 5-Aug-2023)

	Ref	Expression
Assertion	sbid2vw	$$⊢\left[t/x\right]\left[x/t\right]\phi \leftrightarrow \phi$$

Proof

Step	Hyp	Ref	Expression
1		sbequ12r	$$⊢x=t\to \left(\left[x/t\right]\phi \leftrightarrow \phi \right)$$
2	1	sbievw	$$⊢\left[t/x\right]\left[x/t\right]\phi \leftrightarrow \phi$$