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Theorem sa-abvi 31427
Description: A theorem about the universal class. Inference associated with bj-abv 35402 (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 3450 . 2 V = {𝑥𝑥 = 𝑥}
2 equid 2016 . . . 4 𝑥 = 𝑥
3 sa-abvi.1 . . . 4 𝜑
42, 32th 264 . . 3 (𝑥 = 𝑥𝜑)
54abbii 2807 . 2 {𝑥𝑥 = 𝑥} = {𝑥𝜑}
61, 5eqtri 2765 1 V = {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  {cab 2714  Vcvv 3448
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-v 3450
This theorem is referenced by: (None)
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