Theorem ceqsrexv2

Description: Alternate elimitation of a restricted existential quantifier, using implicit substitution. (Contributed by Scott Fenton, 5-Sep-2017)

	Ref	Expression
Hypothesis	ceqsrexv2.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	ceqsrexv2	$$⊢\exists x\in B\left(x=A\wedge \phi \right)\leftrightarrow \left(A\in B\wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		ceqsrexv2.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
2	1	ceqsrexbv	$$⊢\exists x\in B\left(x=A\wedge \phi \right)\leftrightarrow \left(A\in B\wedge \psi \right)$$