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Theorem sssseq 3877
 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 3874 . 2 (𝐴 = 𝐵 ↔ (𝐴𝐵𝐵𝐴))
21rbaibr 530 1 (𝐵𝐴 → (𝐴𝐵𝐴 = 𝐵))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 198   = wceq 1507   ⊆ wss 3830 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-ext 2751 This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-clab 2760  df-cleq 2772  df-clel 2847  df-in 3837  df-ss 3844 This theorem is referenced by:  vdiscusgrb  27015
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