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Theorem imnang 1821
Description: Quantified implication in terms of quantified negation of conjunction. (Contributed by BJ, 16-Jul-2021.)
Assertion
Ref Expression
imnang (∀𝑥(𝜑 → ¬ 𝜓) ↔ ∀𝑥 ¬ (𝜑𝜓))

Proof of Theorem imnang
StepHypRef Expression
1 imnan 400 . 2 ((𝜑 → ¬ 𝜓) ↔ ¬ (𝜑𝜓))
21albii 1799 1 (∀𝑥(𝜑 → ¬ 𝜓) ↔ ∀𝑥 ¬ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 207  wa 396  wal 1518
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1775  ax-4 1789
This theorem depends on definitions:  df-bi 208  df-an 397
This theorem is referenced by:  alinexa  1822  raln  3120  n0el  4235  ballotlem2  31319  wl-dfrexsb  34328
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