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Theorem bj-rabtrALTALT 32575
Description: Alternate proof of bj-rabtr 32573. (Contributed by BJ, 22-Apr-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
bj-rabtrALTALT {𝑥𝐴 ∣ ⊤} = 𝐴
Distinct variable group:   𝑥,𝐴

Proof of Theorem bj-rabtrALTALT
StepHypRef Expression
1 ssrab2 3666 . 2 {𝑥𝐴 ∣ ⊤} ⊆ 𝐴
2 ssid 3603 . . 3 𝐴𝐴
3 tru 1484 . . . 4
43rgenw 2919 . . 3 𝑥𝐴
5 ssrab 3659 . . 3 (𝐴 ⊆ {𝑥𝐴 ∣ ⊤} ↔ (𝐴𝐴 ∧ ∀𝑥𝐴 ⊤))
62, 4, 5mpbir2an 954 . 2 𝐴 ⊆ {𝑥𝐴 ∣ ⊤}
71, 6eqssi 3599 1 {𝑥𝐴 ∣ ⊤} = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  wtru 1481  wral 2907  {crab 2911  wss 3555
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2912  df-rab 2916  df-in 3562  df-ss 3569
This theorem is referenced by: (None)
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