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Theorem bj-rabtr 34391
 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 4007 . 2 {𝑥𝐴 ∣ ⊤} ⊆ 𝐴
2 ssid 3937 . . 3 𝐴𝐴
3 tru 1542 . . . 4
43rgenw 3118 . . 3 𝑥𝐴
5 ssrab 4000 . . 3 (𝐴 ⊆ {𝑥𝐴 ∣ ⊤} ↔ (𝐴𝐴 ∧ ∀𝑥𝐴 ⊤))
62, 4, 5mpbir2an 710 . 2 𝐴 ⊆ {𝑥𝐴 ∣ ⊤}
71, 6eqssi 3931 1 {𝑥𝐴 ∣ ⊤} = 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538  ⊤wtru 1539  ∀wral 3106  {crab 3110   ⊆ wss 3881 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-ral 3111  df-rab 3115  df-v 3443  df-in 3888  df-ss 3898 This theorem is referenced by: (None)
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