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Theorem sssseq 40305
 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 3583 . 2 (𝐴 = 𝐵 ↔ (𝐴𝐵𝐵𝐴))
21rbaibr 944 1 (𝐵𝐴 → (𝐴𝐵𝐴 = 𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 195   = wceq 1475   ⊆ 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-in 3547  df-ss 3554 This theorem is referenced by:  vdiscusgrb  40746
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