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

Theorem bj-nexrt 32807
Description: Closed form of nexr 2100. Contrapositive of 19.8a 2090. (Contributed by BJ, 20-Oct-2019.)
Assertion
Ref Expression
bj-nexrt (¬ ∃𝑥𝜑 → ¬ 𝜑)

Proof of Theorem bj-nexrt
StepHypRef Expression
1 19.8a 2090 . 2 (𝜑 → ∃𝑥𝜑)
21con3i 150 1 (¬ ∃𝑥𝜑 → ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wex 1744
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-ex 1745
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator