Theorem moexex

Description: "At most one" double quantification. Usage of this theorem is discouraged because it depends on ax-13 . Use the version moexexvw when possible. (Contributed by NM, 3-Dec-2001) (Proof shortened by Wolf Lammen, 28-Dec-2018) Factor out common proof lines with moexexvw . (Revised by Wolf Lammen, 2-Oct-2023) (New usage is discouraged.)

	Ref	Expression
Hypothesis	moexex.1	|- F/ y ph
Assertion	moexex	|- ( ( E* x ph /\ A. x E* y ps ) -> E* y E. x ( ph /\ ps ) )

Proof

Step	Hyp	Ref	Expression
1		moexex.1	|- F/ y ph
2	1	nfmo	|- F/ y E* x ph
3		nfe1	|- F/ x E. x ( ph /\ ps )
4	3	nfmo	|- F/ x E* y E. x ( ph /\ ps )
5	1 2 4	moexexlem	|- ( ( E* x ph /\ A. x E* y ps ) -> E* y E. x ( ph /\ ps ) )