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Theorem bj-elssuniab 10296
Description: Version of elssuni 3635 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 (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝐴 {𝑥𝜑}))

Proof of Theorem bj-elssuniab
StepHypRef Expression
1 sbc8g 2793 . 2 (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝐴 ∈ {𝑥𝜑}))
2 elssuni 3635 . 2 (𝐴 ∈ {𝑥𝜑} → 𝐴 {𝑥𝜑})
31, 2syl6bi 156 1 (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝐴 {𝑥𝜑}))
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1409  {cab 2042  wnfc 2181  [wsbc 2786  wss 2944   cuni 3607
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-sbc 2787  df-in 2951  df-ss 2958  df-uni 3608
This theorem is referenced by: (None)
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