Metamath Proof Explorer

Theorem dfss

Description: Variant of subclass definition dfss2 . (Contributed by NM, 21-Jun-1993)

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

Proof

Step Hyp Ref Expression
1 dfss2 
 |-  ( A C_ B <-> ( A i^i B ) = A )
2 eqcom 
 |-  ( ( A i^i B ) = A <-> A = ( A i^i B ) )
3 1 2 bitri 
 |-  ( A C_ B <-> A = ( A i^i B ) )