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Theorem bj-rabtrAUTO 33255
 Description: Proof of bj-rabtr 33252 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 3834 . 2 {𝑥𝐴 ∣ ⊤} ⊆ 𝐴
2 ssid 3771 . . . . 5 𝐴𝐴
32a1i 11 . . . 4 (⊤ → 𝐴𝐴)
4 simpl 468 . . . 4 ((⊤ ∧ 𝑥𝐴) → ⊤)
53, 4ssrabdv 3828 . . 3 (⊤ → 𝐴 ⊆ {𝑥𝐴 ∣ ⊤})
65trud 1640 . 2 𝐴 ⊆ {𝑥𝐴 ∣ ⊤}
71, 6eqssi 3766 1 {𝑥𝐴 ∣ ⊤} = 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1630  ⊤wtru 1631   ∈ wcel 2144  {crab 3064   ⊆ wss 3721 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-ral 3065  df-rab 3069  df-in 3728  df-ss 3735 This theorem is referenced by: (None)
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