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Theorem foo3 23936
Description: A theorem about the universal class. (Contributed by Stefan Allan, 9-Dec-2008.)
Hypothesis
Ref Expression
foo3.1  |-  ph
Assertion
Ref Expression
foo3  |-  _V  =  { x  |  ph }

Proof of Theorem foo3
StepHypRef Expression
1 df-v 2950 . 2  |-  _V  =  { x  |  x  =  x }
2 equid 1688 . . . 4  |-  x  =  x
3 foo3.1 . . . 4  |-  ph
42, 32th 231 . . 3  |-  ( x  =  x  <->  ph )
54abbii 2547 . 2  |-  { x  |  x  =  x }  =  { x  |  ph }
61, 5eqtri 2455 1  |-  _V  =  { x  |  ph }
Colors of variables: wff set class
Syntax hints:    = wceq 1652   {cab 2421   _Vcvv 2948
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-v 2950
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