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Theorem bj-elssuniab 13407
Description: Version of elssuni 3801 using a class abstraction and explicit substitution. (Contributed by BJ, 29-Nov-2019.)
Hypothesis
Ref Expression
bj-elssuniab.nf  |-  F/_ x A
Assertion
Ref Expression
bj-elssuniab  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  ->  A  C_  U. {
x  |  ph }
) )

Proof of Theorem bj-elssuniab
StepHypRef Expression
1 sbc8g 2944 . 2  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  A  e.  { x  |  ph } ) )
2 elssuni 3801 . 2  |-  ( A  e.  { x  | 
ph }  ->  A  C_ 
U. { x  | 
ph } )
31, 2syl6bi 162 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  ->  A  C_  U. {
x  |  ph }
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 2128   {cab 2143   F/_wnfc 2286   [.wsbc 2937    C_ wss 3102   U.cuni 3773
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-sbc 2938  df-in 3108  df-ss 3115  df-uni 3774
This theorem is referenced by: (None)
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