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Theorem bj-nexdh2 34547
Description: Uncurried (imported) form of bj-nexdh 34546. (Contributed by BJ, 6-May-2019.)
Assertion
Ref Expression
bj-nexdh2 ((∀𝑥(𝜑 → ¬ 𝜓) ∧ (𝜒 → ∀𝑥𝜑)) → (𝜒 → ¬ ∃𝑥𝜓))

Proof of Theorem bj-nexdh2
StepHypRef Expression
1 bj-nexdh 34546 . 2 (∀𝑥(𝜑 → ¬ 𝜓) → ((𝜒 → ∀𝑥𝜑) → (𝜒 → ¬ ∃𝑥𝜓)))
21imp 410 1 ((∀𝑥(𝜑 → ¬ 𝜓) ∧ (𝜒 → ∀𝑥𝜑)) → (𝜒 → ¬ ∃𝑥𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 399  wal 1541  wex 1787
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 1817
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788
This theorem is referenced by: (None)
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