Theorem trpredeq2d

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

	Ref	Expression
Hypothesis	trpredeq2d.1	|- ( ph -> A = B )
Assertion	trpredeq2d	|- ( ph -> TrPred ( R , A , X ) = TrPred ( R , B , X ) )

Proof

Step	Hyp	Ref	Expression
1		trpredeq2d.1	|- ( ph -> A = B )
2		trpredeq2	|- ( A = B -> TrPred ( R , A , X ) = TrPred ( R , B , X ) )
3	1 2	syl	|- ( ph -> TrPred ( R , A , X ) = TrPred ( R , B , X ) )