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Theorem bj-elssuniab 13826
Description: Version of elssuni 3824 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 2962 . 2  |-  ( A  e.  V  ->  ( [. A  /  x ]. ph  <->  A  e.  { x  |  ph } ) )
2 elssuni 3824 . 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 2141   {cab 2156   F/_wnfc 2299   [.wsbc 2955    C_ wss 3121   U.cuni 3796
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-sbc 2956  df-in 3127  df-ss 3134  df-uni 3797
This theorem is referenced by: (None)
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