Theorem uneq12d

Description: Equality deduction for the union of two classes. (Contributed by NM, 29-Sep-2004) (Proof shortened by Andrew Salmon, 26-Jun-2011)

	Ref	Expression
Hypotheses	uneq1d.1	|- ( ph -> A = B )
	uneq12d.2	|- ( ph -> C = D )
Assertion	uneq12d	|- ( ph -> ( A u. C ) = ( B u. D ) )

Proof

Step	Hyp	Ref	Expression
1		uneq1d.1	|- ( ph -> A = B )
2		uneq12d.2	|- ( ph -> C = D )
3		uneq12	|- ( ( A = B /\ C = D ) -> ( A u. C ) = ( B u. D ) )
4	1 2 3	syl2anc	|- ( ph -> ( A u. C ) = ( B u. D ) )