Metamath Proof Explorer


Theorem nex

Description: Generalization rule for negated wff. (Contributed by NM, 18-May-1994)

Ref Expression
Hypothesis nex.1
|- -. ph
Assertion nex
|- -. E. x ph

Proof

Step Hyp Ref Expression
1 nex.1
 |-  -. ph
2 alnex
 |-  ( A. x -. ph <-> -. E. x ph )
3 2 1 mpgbi
 |-  -. E. x ph