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Theorem bj-abf 36296
Description: Shorter proof of abf 4397 (which should be kept as abfALT). (Contributed by BJ, 24-Jul-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-abf.1 ¬ 𝜑
Assertion
Ref Expression
bj-abf {𝑥𝜑} = ∅

Proof of Theorem bj-abf
StepHypRef Expression
1 bj-ab0 36295 . 2 (∀𝑥 ¬ 𝜑 → {𝑥𝜑} = ∅)
2 bj-abf.1 . 2 ¬ 𝜑
31, 2mpg 1791 1 {𝑥𝜑} = ∅
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1533  {cab 2703  c0 4317
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-9 2108  ax-ext 2697
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-dif 3946  df-nul 4318
This theorem is referenced by: (None)
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