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Theorem clsbldimp 25088
Description: A class builder defined by an implication. (Contributed by FL, 18-Sep-2010.)
Assertion
Ref Expression
clsbldimp  |-  { x  |  ( ph  ->  ps ) }  =  ( { x  |  -.  ph }  u.  { x  |  ps } )

Proof of Theorem clsbldimp
StepHypRef Expression
1 imor 401 . . 3  |-  ( (
ph  ->  ps )  <->  ( -.  ph  \/  ps ) )
21abbii 2395 . 2  |-  { x  |  ( ph  ->  ps ) }  =  {
x  |  ( -. 
ph  \/  ps ) }
3 unab 3435 . 2  |-  ( { x  |  -.  ph }  u.  { x  |  ps } )  =  { x  |  ( -.  ph  \/  ps ) }
42, 3eqtr4i 2306 1  |-  { x  |  ( ph  ->  ps ) }  =  ( { x  |  -.  ph }  u.  { x  |  ps } )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357    = wceq 1623   {cab 2269    u. cun 3150
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-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157
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