Metamath Proof Explorer

Theorem ineq2

Description: Equality theorem for intersection of two classes. (Contributed by NM, 26-Dec-1993)

Ref Expression
Assertion ineq2 
|- ( A = B -> ( C i^i A ) = ( C i^i B ) )

Proof

Step Hyp Ref Expression
1 ineq1 
 |-  ( A = B -> ( A i^i C ) = ( B i^i C ) )
2 incom 
 |-  ( C i^i A ) = ( A i^i C )
3 incom 
 |-  ( C i^i B ) = ( B i^i C )
4 1 2 3 3eqtr4g 
 |-  ( A = B -> ( C i^i A ) = ( C i^i B ) )