Theorem ifeq12d

Description: Equality deduction for conditional operator. (Contributed by NM, 24-Mar-2015)

	Ref	Expression
Hypotheses	ifeq1d.1	|- ( ph -> A = B )
	ifeq12d.2	|- ( ph -> C = D )
Assertion	ifeq12d	|- ( ph -> if ( ps , A , C ) = if ( ps , B , D ) )

Proof

Step	Hyp	Ref	Expression
1		ifeq1d.1	|- ( ph -> A = B )
2		ifeq12d.2	|- ( ph -> C = D )
3	1	ifeq1d	|- ( ph -> if ( ps , A , C ) = if ( ps , B , C ) )
4	2	ifeq2d	|- ( ph -> if ( ps , B , C ) = if ( ps , B , D ) )
5	3 4	eqtrd	|- ( ph -> if ( ps , A , C ) = if ( ps , B , D ) )