Theorem nex 1546

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 1545	. 2 |- ( A. x -. ph <-> -. E. x ph )
2		nex.1	. 2 |- -. ph
3	1, 2	mpgbi 1498	1 |- -. E. x ph

Syntax hints:   -. wn 3   E.wex 1538

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 617  ax-in2 618  ax-5 1493  ax-gen 1495  ax-ie2 1540

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-fal 1401

This theorem is referenced by:  ru  3027  0nelxp  4747  0xp  4799  dm0  4937  co02  5242  0fv  5665  mpo0  6074  0npr  7670  0g0  13409  gsum0g  13429