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Theorem sssseq 3996
Description: If a class is a subclass of another class, then the classes are equal if and only if 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 3993 . 2 (𝐴 = 𝐵 ↔ (𝐴𝐵𝐵𝐴))
21rbaibr 537 1 (𝐵𝐴 → (𝐴𝐵𝐴 = 𝐵))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 205   = wceq 1534  wss 3945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3472  df-in 3952  df-ss 3962
This theorem is referenced by:  vdiscusgrb  29337  isdomn6  32946
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