Theorem nex 1511

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 1510	. 2 |- ( A. x -. ph <-> -. E. x ph )
2		nex.1	. 2 |- -. ph
3	1, 2	mpgbi 1463	1 |- -. E. x ph

Syntax hints:   -. wn 3   E.wex 1503

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1458  ax-gen 1460  ax-ie2 1505

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370

This theorem is referenced by:  ru  2984  0nelxp  4687  0xp  4739  dm0  4876  co02  5179  0fv  5590  mpo0  5988  0npr  7543  0g0  12959  gsum0g  12979