Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-abbi2i Structured version   Visualization version   GIF version

Theorem bj-abbi2i 33138
Description: Remove dependency on ax-13 2352 from abbi2i 2881. (Contributed by BJ, 23-Jun-2019.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
bj-abbi2i.1 (𝑥𝐴𝜑)
Assertion
Ref Expression
bj-abbi2i 𝐴 = {𝑥𝜑}
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem bj-abbi2i
StepHypRef Expression
1 bj-abeq2 33135 . 2 (𝐴 = {𝑥𝜑} ↔ ∀𝑥(𝑥𝐴𝜑))
2 bj-abbi2i.1 . 2 (𝑥𝐴𝜑)
31, 2mpgbir 1894 1 𝐴 = {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:  wb 197   = wceq 1652  wcel 2155  {cab 2751
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2069  ax-7 2105  ax-9 2164  ax-10 2183  ax-11 2198  ax-12 2211  ax-ext 2743
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-ex 1875  df-nf 1879  df-sb 2062  df-clab 2752  df-cleq 2758  df-clel 2761
This theorem is referenced by:  bj-abid2  33144  bj-termab  33207  bj-df-nul  33376
  Copyright terms: Public domain W3C validator