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Theorem bj-rabtr 36913
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 4090 . 2 {𝑥𝐴 ∣ ⊤} ⊆ 𝐴
2 ssid 4018 . . 3 𝐴𝐴
3 tru 1541 . . . 4
43rgenw 3063 . . 3 𝑥𝐴
5 ssrab 4083 . . 3 (𝐴 ⊆ {𝑥𝐴 ∣ ⊤} ↔ (𝐴𝐴 ∧ ∀𝑥𝐴 ⊤))
62, 4, 5mpbir2an 711 . 2 𝐴 ⊆ {𝑥𝐴 ∣ ⊤}
71, 6eqssi 4012 1 {𝑥𝐴 ∣ ⊤} = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  wtru 1538  wral 3059  {crab 3433  wss 3963
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-11 2155  ax-12 2175  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-nfc 2890  df-ral 3060  df-rab 3434  df-ss 3980
This theorem is referenced by: (None)
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