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Theorem foo3 29628
Description: A theorem about the universal class. (Contributed by Stefan Allan, 9-Dec-2008.)
Hypothesis
Ref Expression
foo3.1 𝜑
Assertion
Ref Expression
foo3 V = {𝑥𝜑}

Proof of Theorem foo3
StepHypRef Expression
1 df-v 3391 . 2 V = {𝑥𝑥 = 𝑥}
2 equid 2108 . . . 4 𝑥 = 𝑥
3 foo3.1 . . . 4 𝜑
42, 32th 255 . . 3 (𝑥 = 𝑥𝜑)
54abbii 2921 . 2 {𝑥𝑥 = 𝑥} = {𝑥𝜑}
61, 5eqtri 2826 1 V = {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1637  {cab 2790  Vcvv 3389
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2068  ax-7 2104  ax-9 2165  ax-10 2185  ax-11 2201  ax-12 2214  ax-ext 2782
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-sb 2061  df-clab 2791  df-cleq 2797  df-clel 2800  df-v 3391
This theorem is referenced by: (None)
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