Theorem expandrex

Description: Expand a restricted existential quantifier to primitives. (Contributed by Rohan Ridenour, 13-Aug-2023)

	Ref	Expression
Hypothesis	expandrex.1	|- ( ph <-> ps )
Assertion	expandrex	|- ( E. x e. A ph <-> -. A. x ( x e. A -> -. ps ) )

Proof

Step	Hyp	Ref	Expression
1		expandrex.1	|- ( ph <-> ps )
2		notnotb	|- ( ps <-> -. -. ps )
3	1 2	bitri	|- ( ph <-> -. -. ps )
4	3	expandrexn	|- ( E. x e. A ph <-> -. A. x ( x e. A -> -. ps ) )