Theorem trpredeq3d

Description: Equality deduction for transitive predecessors. (Contributed by Scott Fenton, 2-Feb-2011)

	Ref	Expression
Hypothesis	trpredeq3d.1	|- ( ph -> X = Y )
Assertion	trpredeq3d	|- ( ph -> TrPred ( R , A , X ) = TrPred ( R , A , Y ) )

Proof

Step	Hyp	Ref	Expression
1		trpredeq3d.1	|- ( ph -> X = Y )
2		trpredeq3	|- ( X = Y -> TrPred ( R , A , X ) = TrPred ( R , A , Y ) )
3	1 2	syl	|- ( ph -> TrPred ( R , A , X ) = TrPred ( R , A , Y ) )