Theorem nex 1524

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 1523	. 2 |- ( A. x -. ph <-> -. E. x ph )
2		nex.1	. 2 |- -. ph
3	1, 2	mpgbi 1476	1 |- -. E. x ph

Syntax hints:   -. wn 3   E.wex 1516

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 1471  ax-gen 1473  ax-ie2 1518

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-fal 1379

This theorem is referenced by:  ru  3004  0nelxp  4721  0xp  4773  dm0  4911  co02  5215  0fv  5635  mpo0  6038  0npr  7631  0g0  13323  gsum0g  13343