Theorem trpredeq2d

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

	Ref	Expression
Hypothesis	trpredeq2d.1	$$⊢\phi \to A=B$$
Assertion	trpredeq2d	$$⊢\phi \to TrPred\left(R,A,X\right)=TrPred\left(R,B,X\right)$$

Proof

Step	Hyp	Ref	Expression
1		trpredeq2d.1	$$⊢\phi \to A=B$$
2		trpredeq2	$$⊢A=B\to TrPred\left(R,A,X\right)=TrPred\left(R,B,X\right)$$
3	1 2	syl	$$⊢\phi \to TrPred\left(R,A,X\right)=TrPred\left(R,B,X\right)$$