Theorem wrecseq2

Description: Equality theorem for the well-ordered recursive function generator. (Contributed by Scott Fenton, 7-Jun-2018)

	Ref	Expression
Assertion	wrecseq2	⊢ ( 𝐴 = 𝐵 → wrecs ( 𝑅 , 𝐴 , 𝐹 ) = wrecs ( 𝑅 , 𝐵 , 𝐹 ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝑅 = 𝑅
2		eqid	⊢ 𝐹 = 𝐹
3		wrecseq123	⊢ ( ( 𝑅 = 𝑅 ∧ 𝐴 = 𝐵 ∧ 𝐹 = 𝐹 ) → wrecs ( 𝑅 , 𝐴 , 𝐹 ) = wrecs ( 𝑅 , 𝐵 , 𝐹 ) )
4	1 2 3	mp3an13	⊢ ( 𝐴 = 𝐵 → wrecs ( 𝑅 , 𝐴 , 𝐹 ) = wrecs ( 𝑅 , 𝐵 , 𝐹 ) )