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Theorem sssseq 3911
 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 3908 . 2 (𝐴 = 𝐵 ↔ (𝐴𝐵𝐵𝐴))
21rbaibr 542 1 (𝐵𝐴 → (𝐴𝐵𝐴 = 𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 209   = wceq 1539   ⊆ wss 3859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-ext 2730 This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1542  df-ex 1783  df-sb 2071  df-clab 2737  df-cleq 2751  df-clel 2831  df-v 3412  df-in 3866  df-ss 3876 This theorem is referenced by:  vdiscusgrb  27420
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