Theorem dfss 3049

Description: Variant of subclass definition df-ss 3048. (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 3048	. 2 |- ( A C_ B <-> ( A i^i B ) = A )
2		eqcom 2115	. 2 |- ( ( A i^i B ) = A <-> A = ( A i^i B ) )
3	1, 2	bitri 183	1 |- ( A C_ B <-> A = ( A i^i B ) )

Syntax hints:   <-> wb 104   = wceq 1312   i^i cin 3034   C_ wss 3035

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1404  ax-gen 1406  ax-ext 2095

This theorem depends on definitions:  df-bi 116  df-cleq 2106  df-ss 3048

This theorem is referenced by:  dfss2  3050  onelini  4310  cnvcnv  4947  funimass1  5156  sbthlemi5  6799  dmaddpi  7075  dmmulpi  7076  tgioo  12526