Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-notalbii Structured version   Visualization version   GIF version

Theorem bj-notalbii 32293
Description: Equivalence of universal quantification of negation of equivalent formulas. Shortens ab0 3931 (103>94), ballotlem2 30373 (2655>2648), bnj1143 30622 (522>519), hausdiag 21388 (2119>2104). (Contributed by BJ, 17-Jul-2021.)
Hypothesis
Ref Expression
bj-notalbii.1 (𝜑𝜓)
Assertion
Ref Expression
bj-notalbii (∀𝑥 ¬ 𝜑 ↔ ∀𝑥 ¬ 𝜓)

Proof of Theorem bj-notalbii
StepHypRef Expression
1 bj-notalbii.1 . . 3 (𝜑𝜓)
21notbii 310 . 2 𝜑 ↔ ¬ 𝜓)
32albii 1744 1 (∀𝑥 ¬ 𝜑 ↔ ∀𝑥 ¬ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wal 1478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734
This theorem depends on definitions:  df-bi 197
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator