Theorem predeq1

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

	Ref	Expression
Assertion	predeq1	$$⊢R=S\to Pred\left(R,A,X\right)=Pred\left(S,A,X\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢A=A$$
2		eqid	$$⊢X=X$$
3		predeq123	$$⊢\left(R=S\wedge A=A\wedge X=X\right)\to Pred\left(R,A,X\right)=Pred\left(S,A,X\right)$$
4	1 2 3	mp3an23	$$⊢R=S\to Pred\left(R,A,X\right)=Pred\left(S,A,X\right)$$