Theorem expandexn

Description: Expand an existential quantifier to primitives while contracting a double negation. (Contributed by Rohan Ridenour, 13-Aug-2023)

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

Proof

Step	Hyp	Ref	Expression
1		expandexn.1	|- ( ph <-> -. ps )
2	1	exbii	|- ( E. x ph <-> E. x -. ps )
3		exnal	|- ( E. x -. ps <-> -. A. x ps )
4	2 3	bitri	|- ( E. x ph <-> -. A. x ps )