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Theorem bj-elssuniab 7037
Description: Version of elssuni 3582 using a class abstraction and explicit substitution. (Contributed by BJ, 29-Nov-2019.)
Hypothesis
Ref Expression
bj-elssuniab.nf xA
Assertion
Ref Expression
bj-elssuniab (A 𝑉 → ([A / x]φA {xφ}))

Proof of Theorem bj-elssuniab
StepHypRef Expression
1 sbc8g 2748 . 2 (A 𝑉 → ([A / x]φA {xφ}))
2 elssuni 3582 . 2 (A {xφ} → A {xφ})
31, 2syl6bi 152 1 (A 𝑉 → ([A / x]φA {xφ}))
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1374  {cab 2008  wnfc 2147  [wsbc 2741  wss 2894   cuni 3554
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-sbc 2742  df-in 2901  df-ss 2908  df-uni 3555
This theorem is referenced by: (None)
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