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Theorem bj-abf 33228
Description: Shorter proof of abf 4122 (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 33227 . 2 (∀𝑥 ¬ 𝜑 → {𝑥𝜑} = ∅)
2 bj-abf.1 . 2 ¬ 𝜑
31, 2mpg 1872 1 {𝑥𝜑} = ∅
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1631  {cab 2757  c0 4063
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-v 3353  df-dif 3726  df-nul 4064
This theorem is referenced by: (None)
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