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Theorem bj-elssuniab 9199
Description: Version of elssuni 3599 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 2765 . 2 (A 𝑉 → ([A / x]φA {xφ}))
2 elssuni 3599 . 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 1390  {cab 2023  wnfc 2162  [wsbc 2758  wss 2911   cuni 3571
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-sbc 2759  df-in 2918  df-ss 2925  df-uni 3572
This theorem is referenced by: (None)
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