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Metamath Proof Explorer

Theorem nexd

Description: Deduction for generalization rule for negated wff. (Contributed by Mario Carneiro, 24-Sep-2016)

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

Proof

Step Hyp Ref Expression
1 nexd.1 
 |-  F/ x ph
2 nexd.2 
 |-  ( ph -> -. ps )
3 1 nf5ri 
 |-  ( ph -> A. x ph )
4 3 2 nexdh 
 |-  ( ph -> -. E. x ps )