Theorem sbequ12r

Description: An equality theorem for substitution. (Contributed by NM, 6-Oct-2004) (Proof shortened by Andrew Salmon, 21-Jun-2011)

	Ref	Expression
Assertion	sbequ12r	$$⊢x=y\to \left(\left[x/y\right]\phi \leftrightarrow \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		sbequ12	$$⊢y=x\to \left(\phi \leftrightarrow \left[x/y\right]\phi \right)$$
2	1	bicomd	$$⊢y=x\to \left(\left[x/y\right]\phi \leftrightarrow \phi \right)$$
3	2	equcoms	$$⊢x=y\to \left(\left[x/y\right]\phi \leftrightarrow \phi \right)$$