Theorem sbcov

Description: A composition law for substitution. Version of sbco with a disjoint variable condition using fewer axioms. (Contributed by NM, 14-May-1993) (Revised by GG, 7-Aug-2023) (Proof shortened by SN, 26-Aug-2025)

	Ref	Expression
Assertion	sbcov	$$⊢\left[y/x\right]\left[x/y\right]\phi \leftrightarrow \left[y/x\right]\phi$$

Proof

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