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Theorem foo3 29169
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 3191 . 2 V = {𝑥𝑥 = 𝑥}
2 equid 1936 . . . 4 𝑥 = 𝑥
3 foo3.1 . . . 4 𝜑
42, 32th 254 . . 3 (𝑥 = 𝑥𝜑)
54abbii 2736 . 2 {𝑥𝑥 = 𝑥} = {𝑥𝜑}
61, 5eqtri 2643 1 V = {𝑥𝜑}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  {cab 2607  Vcvv 3189
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-v 3191
This theorem is referenced by: (None)
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