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Theorem sa-abvi 30230
Description: A theorem about the universal class. Inference associated with bj-abv 34348 (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 3446 . 2 V = {𝑥𝑥 = 𝑥}
2 equid 2019 . . . 4 𝑥 = 𝑥
3 sa-abvi.1 . . . 4 𝜑
42, 32th 267 . . 3 (𝑥 = 𝑥𝜑)
54abbii 2866 . 2 {𝑥𝑥 = 𝑥} = {𝑥𝜑}
61, 5eqtri 2824 1 V = {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1538  {cab 2779  Vcvv 3444
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-9 2122  ax-ext 2773
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-v 3446
This theorem is referenced by: (None)
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