Theorem ssrabeq 3585

Description: If the restricting class of a restricted class abstraction is a subset of this restricted class abstraction, it is equal to this restricted class abstraction. (Contributed by Alexander van der Vekens, 31-Dec-2017.)

Assertion

Ref	Expression
ssrabeq

Distinct variable group:   ,

Proof of Theorem ssrabeq

Step	Hyp	Ref	Expression
1		ssrab2 3584	. . 3
2	1	biantru 505	. 2
3		eqss 3518	. 2
4	2, 3	bitr4i 252	1

Syntax hints:  <->wb 184  /\wa 369  =wceq 1395  {crab 2811  C_wss 3475

This theorem is referenced by:  difrab0eq  3887

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-in 3482  df-ss 3489