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Theorem nex 1477
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
StepHypRef Expression
1 alnex 1476 . 2  |-  ( A. x  -.  ph  <->  -.  E. x ph )
2 nex.1 . 2  |-  -.  ph
31, 2mpgbi 1429 1  |-  -.  E. x ph
Colors of variables: wff set class
Syntax hints:   -. wn 3   E.wex 1469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-5 1424  ax-gen 1426  ax-ie2 1471
This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338
This theorem is referenced by:  ru  2911  0nelxp  4574  0xp  4626  dm0  4760  co02  5059  0fv  5463  mpo0  5848  0npr  7314
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