Theorem nfeud2

Description: Bound-variable hypothesis builder for uniqueness. (Contributed by Mario Carneiro, 14-Nov-2016) (Proof shortened by Wolf Lammen, 4-Oct-2018) (Proof shortened by BJ, 14-Oct-2022) Usage of this theorem is discouraged because it depends on ax-13 . Use nfeudw instead. (New usage is discouraged.)

	Ref	Expression
Hypotheses	nfeud2.1	|- F/ y ph
	nfeud2.2	|- ( ( ph /\ -. A. x x = y ) -> F/ x ps )
Assertion	nfeud2	|- ( ph -> F/ x E! y ps )

Proof

Step	Hyp	Ref	Expression
1		nfeud2.1	|- F/ y ph
2		nfeud2.2	|- ( ( ph /\ -. A. x x = y ) -> F/ x ps )
3		df-eu	|- ( E! y ps <-> ( E. y ps /\ E* y ps ) )
4	1 2	nfexd2	|- ( ph -> F/ x E. y ps )
5	1 2	nfmod2	|- ( ph -> F/ x E* y ps )
6	4 5	nfand	|- ( ph -> F/ x ( E. y ps /\ E* y ps ) )
7	3 6	nfxfrd	|- ( ph -> F/ x E! y ps )