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Theorem bj-rabtrAUTO 32121
 Description: Proof of bj-rabtr 32118 found automatically by "improve all /depth 3 /3" followed by "minimize *". (Contributed by BJ, 22-Apr-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
bj-rabtrAUTO {𝑥𝐴 ∣ ⊤} = 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem bj-rabtrAUTO
StepHypRef Expression
1 ssrab2 3650 . 2 {𝑥𝐴 ∣ ⊤} ⊆ 𝐴
2 ssid 3587 . . . . 5 𝐴𝐴
32a1i 11 . . . 4 (⊤ → 𝐴𝐴)
4 simpl 472 . . . 4 ((⊤ ∧ 𝑥𝐴) → ⊤)
53, 4ssrabdv 3644 . . 3 (⊤ → 𝐴 ⊆ {𝑥𝐴 ∣ ⊤})
65trud 1484 . 2 𝐴 ⊆ {𝑥𝐴 ∣ ⊤}
71, 6eqssi 3584 1 {𝑥𝐴 ∣ ⊤} = 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  ⊤wtru 1476   ∈ wcel 1977  {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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