Theorem trpredeq1d

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

	Ref	Expression
Hypothesis	trpredeq1d.1	$$⊢\phi \to R=S$$
Assertion	trpredeq1d	$$⊢\phi \to TrPred\left(R,A,X\right)=TrPred\left(S,A,X\right)$$

Proof

Step	Hyp	Ref	Expression
1		trpredeq1d.1	$$⊢\phi \to R=S$$
2		trpredeq1	$$⊢R=S\to TrPred\left(R,A,X\right)=TrPred\left(S,A,X\right)$$
3	1 2	syl	$$⊢\phi \to TrPred\left(R,A,X\right)=TrPred\left(S,A,X\right)$$