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Theorem nexdh 1589
Description: Deduction for generalization rule for negated wff. (Contributed by NM, 2-Jan-2002.)
Hypotheses
Ref Expression
nexdh.1 (φxφ)
nexdh.2 (φ → ¬ ψ)
Assertion
Ref Expression
nexdh (φ → ¬ xψ)

Proof of Theorem nexdh
StepHypRef Expression
1 nexdh.1 . . 3 (φxφ)
2 nexdh.2 . . 3 (φ → ¬ ψ)
31, 2alrimih 1565 . 2 (φx ¬ ψ)
4 alnex 1543 . 2 (x ¬ ψ ↔ ¬ xψ)
53, 4sylib 188 1 (φ → ¬ xψ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1540  wex 1541
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by:  nexd  1771
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