Metamath Proof Explorer

Theorem difeq12

Description: Equality theorem for class difference. (Contributed by FL, 31-Aug-2009)

Ref Expression
Assertion difeq12 
|- ( ( A = B /\ C = D ) -> ( A \ C ) = ( B \ D ) )

Proof

Step Hyp Ref Expression
1 difeq1 
 |-  ( A = B -> ( A \ C ) = ( B \ C ) )
2 difeq2 
 |-  ( C = D -> ( B \ C ) = ( B \ D ) )
3 1 2 sylan9eq 
 |-  ( ( A = B /\ C = D ) -> ( A \ C ) = ( B \ D ) )