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Theorem dfss5OLD 3781
Description: Obsolete as of 22-Jul-2021. (Contributed by David Moews, 1-May-2017.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
dfss5OLD (𝐴𝐵𝐴 = (𝐵𝐴))

Proof of Theorem dfss5OLD
StepHypRef Expression
1 sseqin2 3779 . 2 (𝐴𝐵 ↔ (𝐵𝐴) = 𝐴)
2 eqcom 2617 . 2 ((𝐵𝐴) = 𝐴𝐴 = (𝐵𝐴))
31, 2bitri 263 1 (𝐴𝐵𝐴 = (𝐵𝐴))
Colors of variables: wff setvar class
Syntax hints:  wb 195   = wceq 1475  cin 3539  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-v 3175  df-in 3547  df-ss 3554
This theorem is referenced by: (None)
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