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Theorem foo3 23023
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 2790 . 2  |-  _V  =  { x  |  x  =  x }
2 equid 1644 . . . 4  |-  x  =  x
3 foo3.1 . . . 4  |-  ph
42, 32th 230 . . 3  |-  ( x  =  x  <->  ph )
54abbii 2395 . 2  |-  { x  |  x  =  x }  =  { x  |  ph }
61, 5eqtri 2303 1  |-  _V  =  { x  |  ph }
Colors of variables: wff set class
Syntax hints:    = wceq 1623   {cab 2269   _Vcvv 2788
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-v 2790
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