Metamath Proof Explorer


Theorem dfss

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

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

Proof

Step Hyp Ref Expression
1 df-ss
 |-  ( 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 ) )