Theorem eqsb1

Description: Substitution for the left-hand side in an equality. Class version of equsb3 . (Contributed by Rodolfo Medina, 28-Apr-2010)

	Ref	Expression
Assertion	eqsb1	$$⊢\left[y/x\right]x=A\leftrightarrow y=A$$

Proof

Step	Hyp	Ref	Expression
1		eqeq1	$$⊢x=w\to \left(x=A\leftrightarrow w=A\right)$$
2		eqeq1	$$⊢w=y\to \left(w=A\leftrightarrow y=A\right)$$
3	1 2	sbievw2	$$⊢\left[y/x\right]x=A\leftrightarrow y=A$$