Theorem sbcovOLD

Description: Obsolete version of sbcov as of 26-Aug-2025. (Contributed by NM, 14-May-1993) (Revised by GG, 7-Aug-2023) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		sbcom3vv	$$⊢\left[y/x\right]\left[x/y\right]\phi \leftrightarrow \left[y/x\right]\left[y/y\right]\phi$$
2		sbid	$$⊢\left[y/y\right]\phi \leftrightarrow \phi$$
3	2	sbbii	$$⊢\left[y/x\right]\left[y/y\right]\phi \leftrightarrow \left[y/x\right]\phi$$
4	1 3	bitri	$$⊢\left[y/x\right]\left[x/y\right]\phi \leftrightarrow \left[y/x\right]\phi$$