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Theorem bj-rabtrAUTO 31917
Description: Proof of bj-rabtr 31914 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 3649 . 2 {𝑥𝐴 ∣ ⊤} ⊆ 𝐴
2 ssid 3586 . . . . 5 𝐴𝐴
32a1i 11 . . . 4 (⊤ → 𝐴𝐴)
4 simpl 471 . . . 4 ((⊤ ∧ 𝑥𝐴) → ⊤)
53, 4ssrabdv 3643 . . 3 (⊤ → 𝐴 ⊆ {𝑥𝐴 ∣ ⊤})
65trud 1483 . 2 𝐴 ⊆ {𝑥𝐴 ∣ ⊤}
71, 6eqssi 3583 1 {𝑥𝐴 ∣ ⊤} = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  wtru 1475  wcel 1976  {crab 2899  wss 3539
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-ral 2900  df-rab 2904  df-in 3546  df-ss 3553
This theorem is referenced by: (None)
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