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Theorem nexd 1501
Description: Deduction for generalization rule for negated wff. (Contributed by NM, 2-Jan-2002.)
Hypotheses
Ref Expression
nexd.1 (φxφ)
nexd.2 (φ → ¬ ψ)
Assertion
Ref Expression
nexd (φ → ¬ xψ)

Proof of Theorem nexd
StepHypRef Expression
1 nexd.1 . . 3 (φxφ)
2 nexd.2 . . 3 (φ → ¬ ψ)
31, 2alrimih 1355 . 2 (φx ¬ ψ)
4 alnex 1385 . 2 (x ¬ ψ ↔ ¬ xψ)
53, 4sylib 127 1 (φ → ¬ xψ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wal 1240  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-ie2 1380
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248
This theorem is referenced by:  nexdv  1808
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