Theorem sbequvvOLD

Description: Obsolete version of sbequ as of 7-Jul-2023. Version of sbequ with disjoint variable conditions, not requiring ax-13 . (Contributed by Wolf Lammen, 19-Jan-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	sbequvvOLD	$$⊢x=y\to \left(\left[x/z\right]\phi \leftrightarrow \left[y/z\right]\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		sbequivvOLD	$$⊢x=y\to \left(\left[x/z\right]\phi \to \left[y/z\right]\phi \right)$$
2		sbequivvOLD	$$⊢y=x\to \left(\left[y/z\right]\phi \to \left[x/z\right]\phi \right)$$
3	2	equcoms	$$⊢x=y\to \left(\left[y/z\right]\phi \to \left[x/z\right]\phi \right)$$
4	1 3	impbid	$$⊢x=y\to \left(\left[x/z\right]\phi \leftrightarrow \left[y/z\right]\phi \right)$$