Theorem trpredeq3d

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

	Ref	Expression
Hypothesis	trpredeq3d.1	$$⊢\phi \to X=Y$$
Assertion	trpredeq3d	$$⊢\phi \to TrPred\left(R,A,X\right)=TrPred\left(R,A,Y\right)$$

Proof

Step	Hyp	Ref	Expression
1		trpredeq3d.1	$$⊢\phi \to X=Y$$
2		trpredeq3	$$⊢X=Y\to TrPred\left(R,A,X\right)=TrPred\left(R,A,Y\right)$$
3	1 2	syl	$$⊢\phi \to TrPred\left(R,A,X\right)=TrPred\left(R,A,Y\right)$$