Theorem eliminable2b

Description: A theorem used to prove the base case of the Eliminability Theorem (see section comment). (Contributed by BJ, 19-Oct-2019) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	eliminable2b	$$⊢\left\{x|\phi \right\}=y\leftrightarrow \forall z\left(z\in \left\{x|\phi \right\}\leftrightarrow z\in y\right)$$

Proof

Step	Hyp	Ref	Expression
1		dfcleq	$$⊢\left\{x|\phi \right\}=y\leftrightarrow \forall z\left(z\in \left\{x|\phi \right\}\leftrightarrow z\in y\right)$$