Theorem trpredeq1d

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

	Ref	Expression
Hypothesis	trpredeq1d.1	|- ( ph -> R = S )
Assertion	trpredeq1d	|- ( ph -> TrPred ( R , A , X ) = TrPred ( S , A , X ) )

Proof

Step	Hyp	Ref	Expression
1		trpredeq1d.1	|- ( ph -> R = S )
2		trpredeq1	|- ( R = S -> TrPred ( R , A , X ) = TrPred ( S , A , X ) )
3	1 2	syl	|- ( ph -> TrPred ( R , A , X ) = TrPred ( S , A , X ) )