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

Theorem bj-abf 33211
Description: Shorter proof of abf 4176 (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 33210 . 2 (∀𝑥 ¬ 𝜑 → {𝑥𝜑} = ∅)
2 bj-abf.1 . 2 ¬ 𝜑
31, 2mpg 1879 1 {𝑥𝜑} = ∅
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1637  {cab 2792  c0 4116
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2068  ax-7 2104  ax-9 2165  ax-10 2185  ax-11 2201  ax-12 2214  ax-13 2420  ax-ext 2784
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2061  df-clab 2793  df-cleq 2799  df-clel 2802  df-nfc 2937  df-v 3393  df-dif 3772  df-nul 4117
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator