Metamath Proof Explorer

Theorem ineq12

Description: Equality theorem for intersection of two classes. (Contributed by NM, 8-May-1994)

Ref Expression
Assertion ineq12 
|- ( ( A = B /\ C = D ) -> ( A i^i C ) = ( B i^i D ) )

Proof

Step Hyp Ref Expression
1 ineq1 
 |-  ( A = B -> ( A i^i C ) = ( B i^i C ) )
2 ineq2 
 |-  ( C = D -> ( B i^i C ) = ( B i^i D ) )
3 1 2 sylan9eq 
 |-  ( ( A = B /\ C = D ) -> ( A i^i C ) = ( B i^i D ) )