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Theorem bj-elssuniab 9930
 Description: Version of elssuni 3608 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 2771 . 2 (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝐴 ∈ {𝑥𝜑}))
2 elssuni 3608 . 2 (𝐴 ∈ {𝑥𝜑} → 𝐴 {𝑥𝜑})
31, 2syl6bi 152 1 (𝐴𝑉 → ([𝐴 / 𝑥]𝜑𝐴 {𝑥𝜑}))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1393  {cab 2026  Ⅎwnfc 2165  [wsbc 2764   ⊆ wss 2917  ∪ cuni 3580 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-sbc 2765  df-in 2924  df-ss 2931  df-uni 3581 This theorem is referenced by: (None)
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