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Theorem foo3 23794
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 2901 . 2  |-  _V  =  { x  |  x  =  x }
2 equid 1683 . . . 4  |-  x  =  x
3 foo3.1 . . . 4  |-  ph
42, 32th 231 . . 3  |-  ( x  =  x  <->  ph )
54abbii 2499 . 2  |-  { x  |  x  =  x }  =  { x  |  ph }
61, 5eqtri 2407 1  |-  _V  =  { x  |  ph }
Colors of variables: wff set class
Syntax hints:    = wceq 1649   {cab 2373   _Vcvv 2899
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2368
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2374  df-cleq 2380  df-v 2901
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