Theorem sssseq 3621

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	|- ( B C_ A -> ( A C_ B <-> A = B ) )

Proof of Theorem sssseq

Step	Hyp	Ref	Expression
1		eqss 3618	. 2 |- ( A = B <-> ( A C_ B /\ B C_ A ) )
2	1	rbaibr 946	1 |- ( B C_ A -> ( A C_ B <-> A = B ) )

Syntax hints:   -> wi 4   <-> wb 196   = wceq 1483   C_ wss 3574

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-in 3581  df-ss 3588

This theorem is referenced by:  vdiscusgrb  26426