Theorem dfss 3135

Description: Variant of subclass definition df-ss 3134. (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 3134	. 2 |- ( A C_ B <-> ( A i^i B ) = A )
2		eqcom 2172	. 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 1348   i^i cin 3120   C_ wss 3121

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-cleq 2163  df-ss 3134

This theorem is referenced by:  dfss2  3136  onelini  4415  cnvcnv  5063  funimass1  5275  sbthlemi5  6938  dmaddpi  7287  dmmulpi  7288  tgioo  13340