Theorem wsuceq1

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

	Ref	Expression
Assertion	wsuceq1	⊢ ( 𝑅 = 𝑆 → wsuc ( 𝑅 , 𝐴 , 𝑋 ) = wsuc ( 𝑆 , 𝐴 , 𝑋 ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝐴 = 𝐴
2		eqid	⊢ 𝑋 = 𝑋
3		wsuceq123	⊢ ( ( 𝑅 = 𝑆 ∧ 𝐴 = 𝐴 ∧ 𝑋 = 𝑋 ) → wsuc ( 𝑅 , 𝐴 , 𝑋 ) = wsuc ( 𝑆 , 𝐴 , 𝑋 ) )
4	1 2 3	mp3an23	⊢ ( 𝑅 = 𝑆 → wsuc ( 𝑅 , 𝐴 , 𝑋 ) = wsuc ( 𝑆 , 𝐴 , 𝑋 ) )