Theorem wrecseq3

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

	Ref	Expression
Assertion	wrecseq3	⊢ ( 𝐹 = 𝐺 → wrecs ( 𝑅 , 𝐴 , 𝐹 ) = wrecs ( 𝑅 , 𝐴 , 𝐺 ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 𝑅 = 𝑅
2		eqid	⊢ 𝐴 = 𝐴
3		wrecseq123	⊢ ( ( 𝑅 = 𝑅 ∧ 𝐴 = 𝐴 ∧ 𝐹 = 𝐺 ) → wrecs ( 𝑅 , 𝐴 , 𝐹 ) = wrecs ( 𝑅 , 𝐴 , 𝐺 ) )
4	1 2 3	mp3an12	⊢ ( 𝐹 = 𝐺 → wrecs ( 𝑅 , 𝐴 , 𝐹 ) = wrecs ( 𝑅 , 𝐴 , 𝐺 ) )