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Theorem sssseq 3605
Description: If a class is a subclass of another class, the classes are equal iff the other class is a subclass of the first class. (Contributed by AV, 23-Dec-2020.)
Assertion
Ref Expression
sssseq (𝐵𝐴 → (𝐴𝐵𝐴 = 𝐵))

Proof of Theorem sssseq
StepHypRef Expression
1 eqss 3602 . 2 (𝐴 = 𝐵 ↔ (𝐴𝐵𝐵𝐴))
21rbaibr 945 1 (𝐵𝐴 → (𝐴𝐵𝐴 = 𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196   = wceq 1480  wss 3559
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-in 3566  df-ss 3573
This theorem is referenced by:  vdiscusgrb  26325
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