Users' Mathboxes Mathbox for Stefan Allan < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sa-abvi Structured version   Visualization version   GIF version

Theorem sa-abvi 32472
Description: A theorem about the universal class. Inference associated with bj-abv 36889 (which is proved from fewer axioms). (Contributed by Stefan Allan, 9-Dec-2008.)
Hypothesis
Ref Expression
sa-abvi.1 𝜑
Assertion
Ref Expression
sa-abvi V = {𝑥𝜑}

Proof of Theorem sa-abvi
StepHypRef Expression
1 df-v 3480 . 2 V = {𝑥𝑥 = 𝑥}
2 equid 2009 . . . 4 𝑥 = 𝑥
3 sa-abvi.1 . . . 4 𝜑
42, 32th 264 . . 3 (𝑥 = 𝑥𝜑)
54abbii 2807 . 2 {𝑥𝑥 = 𝑥} = {𝑥𝜑}
61, 5eqtri 2763 1 V = {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  {cab 2712  Vcvv 3478
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-9 2116  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-v 3480
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator