Theorem dfss 2932

Description: Variant of subclass definition df-ss 2931. (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 2931	. 2 |- ( A C_ B <-> ( A i^i B ) = A )
2		eqcom 2042	. 2 |- ( ( A i^i B ) = A <-> A = ( A i^i B ) )
3	1, 2	bitri 173	1 |- ( A C_ B <-> A = ( A i^i B ) )

Syntax hints:   <-> wb 98   = wceq 1243   i^i cin 2916   C_ wss 2917

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-ss 2931

This theorem is referenced by:  dfss2  2934  onelini  4167  cnvcnv  4773  funimass1  4976  dmaddpi  6423  dmmulpi  6424