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Theorem sa-abvi 29888
 Description: A theorem about the universal class. Inference associated with bj-abv 33486 (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 3399 . 2 V = {𝑥𝑥 = 𝑥}
2 equid 2058 . . . 4 𝑥 = 𝑥
3 sa-abvi.1 . . . 4 𝜑
42, 32th 256 . . 3 (𝑥 = 𝑥𝜑)
54abbii 2907 . 2 {𝑥𝑥 = 𝑥} = {𝑥𝜑}
61, 5eqtri 2801 1 V = {𝑥𝜑}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1601  {cab 2762  Vcvv 3397 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2054  ax-9 2115  ax-ext 2753 This theorem depends on definitions:  df-bi 199  df-an 387  df-tru 1605  df-ex 1824  df-sb 2012  df-clab 2763  df-cleq 2769  df-v 3399 This theorem is referenced by: (None)
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