Theorem predeq2

Description: Equality theorem for the predecessor class. (Contributed by Scott Fenton, 2-Feb-2011)

	Ref	Expression
Assertion	predeq2	$$⊢A=B\to Pred\left(R,A,X\right)=Pred\left(R,B,X\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢R=R$$
2		eqid	$$⊢X=X$$
3		predeq123	$$⊢\left(R=R\wedge A=B\wedge X=X\right)\to Pred\left(R,A,X\right)=Pred\left(R,B,X\right)$$
4	1 2 3	mp3an13	$$⊢A=B\to Pred\left(R,A,X\right)=Pred\left(R,B,X\right)$$