Theorem clelsb1

Description: Substitution for the first argument of the membership predicate in an atomic formula (class version of elsb1 ). (Contributed by Rodolfo Medina, 28-Apr-2010) (Proof shortened by Andrew Salmon, 14-Jun-2011)

	Ref	Expression
Assertion	clelsb1	$$⊢\left[y/x\right]x\in A\leftrightarrow y\in A$$

Proof

Step	Hyp	Ref	Expression
1		eleq1w	$$⊢x=w\to \left(x\in A\leftrightarrow w\in A\right)$$
2		eleq1w	$$⊢w=y\to \left(w\in A\leftrightarrow y\in A\right)$$
3	1 2	sbievw2	$$⊢\left[y/x\right]x\in A\leftrightarrow y\in A$$