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Theorem bj-adjfrombun 37047
Description: Adjunction from singleton and binary union. (Contributed by BJ, 19-Jan-2025.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-adjfrombun (𝑥 ∪ {𝑦}) ∈ V

Proof of Theorem bj-adjfrombun
StepHypRef Expression
1 vex 3484 . 2 𝑥 ∈ V
2 bj-snexg 37035 . . 3 (𝑦 ∈ V → {𝑦} ∈ V)
32elv 3485 . 2 {𝑦} ∈ V
4 bj-unexg 37039 . 2 ((𝑥 ∈ V ∧ {𝑦} ∈ V) → (𝑥 ∪ {𝑦}) ∈ V)
51, 3, 4mp2an 692 1 (𝑥 ∪ {𝑦}) ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2108  Vcvv 3480  cun 3949  {csn 4626
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-12 2177  ax-ext 2708  ax-bj-sn 37034  ax-bj-bun 37038
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-un 3956  df-sn 4627
This theorem is referenced by: (None)
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