Theorem wsuceq1

Description: Equality theorem for well-founded successor. (Contributed by Scott Fenton, 13-Jun-2018)

	Ref	Expression
Assertion	wsuceq1	$$⊢R=S\to wsuc\left(R,A,X\right)=wsuc\left(S,A,X\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢A=A$$
2		eqid	$$⊢X=X$$
3		wsuceq123	$$⊢\left(R=S\wedge A=A\wedge X=X\right)\to wsuc\left(R,A,X\right)=wsuc\left(S,A,X\right)$$
4	1 2 3	mp3an23	$$⊢R=S\to wsuc\left(R,A,X\right)=wsuc\left(S,A,X\right)$$