Theorem dfss 3261

Description: Variant of subclass definition df-ss 3260. (Contributed by NM, 3-Sep-2004.)

Assertion

Ref	Expression
dfss	|- (A C_ B <-> A = (A i^i B))

Proof of Theorem dfss

Step	Hyp	Ref	Expression
1		df-ss 3260	. 2 |- (A C_ B <-> (A i^i B) = A)
2		eqcom 2355	. 2 |- ((A i^i B) = A <-> A = (A i^i B))
3	1, 2	bitri 240	1 |- (A C_ B <-> A = (A i^i B))

Syntax hints:   <-> wb 176   = wceq 1642   i^i cin 3209   C_ wss 3258

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-cleq 2346  df-ss 3260

This theorem is referenced by:  dfss2  3263  iinrab2  4030  funimass1  5170