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Theorem bj-rabtr 36931
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 4080 . 2 {𝑥𝐴 ∣ ⊤} ⊆ 𝐴
2 ssid 4006 . . 3 𝐴𝐴
3 tru 1544 . . . 4
43rgenw 3065 . . 3 𝑥𝐴
5 ssrab 4073 . . 3 (𝐴 ⊆ {𝑥𝐴 ∣ ⊤} ↔ (𝐴𝐴 ∧ ∀𝑥𝐴 ⊤))
62, 4, 5mpbir2an 711 . 2 𝐴 ⊆ {𝑥𝐴 ∣ ⊤}
71, 6eqssi 4000 1 {𝑥𝐴 ∣ ⊤} = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  wtru 1541  wral 3061  {crab 3436  wss 3951
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-10 2141  ax-11 2157  ax-12 2177  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-nfc 2892  df-ral 3062  df-rab 3437  df-ss 3968
This theorem is referenced by: (None)
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