Metamath Proof Explorer

Theorem uneq12

Description: Equality theorem for the union of two classes. (Contributed by NM, 29-Mar-1998)

Ref Expression
Assertion uneq12 
|- ( ( A = B /\ C = D ) -> ( A u. C ) = ( B u. D ) )

Proof

Step Hyp Ref Expression
1 uneq1 
 |-  ( A = B -> ( A u. C ) = ( B u. C ) )
2 uneq2 
 |-  ( C = D -> ( B u. C ) = ( B u. D ) )
3 1 2 sylan9eq 
 |-  ( ( A = B /\ C = D ) -> ( A u. C ) = ( B u. D ) )