Theorem nex 1459

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

Hypothesis

Ref	Expression
nex.1	|- -. ph

Assertion

Ref	Expression
nex	|- -. E. x ph

Proof of Theorem nex

Step	Hyp	Ref	Expression
1		alnex 1458	. 2 |- ( A. x -. ph <-> -. E. x ph )
2		nex.1	. 2 |- -. ph
3	1, 2	mpgbi 1411	1 |- -. E. x ph

Syntax hints:   -. wn 3   E.wex 1451

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-5 1406  ax-gen 1408  ax-ie2 1453

This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320

This theorem is referenced by:  ru  2877  0nelxp  4527  0xp  4579  dm0  4713  co02  5010  0fv  5410  mpo0  5795  0npr  7239