Metamath Proof Explorer


Theorem nfeud

Description: Bound-variable hypothesis builder for the unique existential quantifier. Deduction version of nfeu . Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfeudw when possible. (Contributed by NM, 15-Feb-2013) (Revised by Mario Carneiro, 7-Oct-2016) (New usage is discouraged.)

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

Proof

Step Hyp Ref Expression
1 nfeud.1
 |-  F/ y ph
2 nfeud.2
 |-  ( ph -> F/ x ps )
3 2 adantr
 |-  ( ( ph /\ -. A. x x = y ) -> F/ x ps )
4 1 3 nfeud2
 |-  ( ph -> F/ x E! y ps )