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Theorem bj-elssuniab 11033
Description: Version of elssuni 3655 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 2833 . 2  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  A  e.  { x  |  ph } ) )
2 elssuni 3655 . 2  |-  ( A  e.  { x  | 
ph }  ->  A  C_ 
U. { x  | 
ph } )
31, 2syl6bi 161 1  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  ->  A  C_  U. {
x  |  ph }
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   {cab 2069   F/_wnfc 2210   [.wsbc 2826    C_ wss 2984   U.cuni 3627
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2614  df-sbc 2827  df-in 2990  df-ss 2997  df-uni 3628
This theorem is referenced by: (None)
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