Theorem sbequ12

Description: An equality theorem for substitution. (Contributed by NM, 14-May-1993)

	Ref	Expression
Assertion	sbequ12	$$⊢x=y\to \left(\phi \leftrightarrow \left[y/x\right]\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		sbequ1	$$⊢x=y\to \left(\phi \to \left[y/x\right]\phi \right)$$
2		sbequ2	$$⊢x=y\to \left(\left[y/x\right]\phi \to \phi \right)$$
3	1 2	impbid	$$⊢x=y\to \left(\phi \leftrightarrow \left[y/x\right]\phi \right)$$