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Theorem bj-rabtr 32118
 Description: Restricted class abstraction with true formula. (Contributed by BJ, 22-Apr-2019.)
Assertion
Ref Expression
bj-rabtr {𝑥𝐴 ∣ ⊤} = 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem bj-rabtr
StepHypRef Expression
1 ssrab2 3650 . 2 {𝑥𝐴 ∣ ⊤} ⊆ 𝐴
2 ssid 3587 . . 3 𝐴𝐴
3 tru 1479 . . . 4
43rgenw 2908 . . 3 𝑥𝐴
5 ssrab 3643 . . 3 (𝐴 ⊆ {𝑥𝐴 ∣ ⊤} ↔ (𝐴𝐴 ∧ ∀𝑥𝐴 ⊤))
62, 4, 5mpbir2an 957 . 2 𝐴 ⊆ {𝑥𝐴 ∣ ⊤}
71, 6eqssi 3584 1 {𝑥𝐴 ∣ ⊤} = 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  ⊤wtru 1476  ∀wral 2896  {crab 2900   ⊆ wss 3540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rab 2905  df-in 3547  df-ss 3554 This theorem is referenced by: (None)
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