Theorem dfss 2987

Description: Variant of subclass definition df-ss 2986. (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 2986	. 2 |- ( A C_ B <-> ( A i^i B ) = A )
2		eqcom 2083	. 2 |- ( ( A i^i B ) = A <-> A = ( A i^i B ) )
3	1, 2	bitri 182	1 |- ( A C_ B <-> A = ( A i^i B ) )

Syntax hints:   <-> wb 103   = wceq 1284   i^i cin 2972   C_ wss 2973

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-cleq 2074  df-ss 2986

This theorem is referenced by:  dfss2  2988  onelini  4185  cnvcnv  4793  funimass1  4996  dmaddpi  6515  dmmulpi  6516