Theorem eqeqan12rd

Description: A useful inference for substituting definitions into an equality. (Contributed by NM, 9-Aug-1994)

	Ref	Expression
Hypotheses	eqeqan12rd.1	|- ( ph -> A = B )
	eqeqan12rd.2	|- ( ps -> C = D )
Assertion	eqeqan12rd	|- ( ( ps /\ ph ) -> ( A = C <-> B = D ) )

Proof

Step	Hyp	Ref	Expression
1		eqeqan12rd.1	|- ( ph -> A = B )
2		eqeqan12rd.2	|- ( ps -> C = D )
3	1 2	eqeqan12d	|- ( ( ph /\ ps ) -> ( A = C <-> B = D ) )
4	3	ancoms	|- ( ( ps /\ ph ) -> ( A = C <-> B = D ) )