Theorem wrecseq3

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

	Ref	Expression
Assertion	wrecseq3	$$⊢F=G\to \mathrm{wrecs}\left(R,A,F\right)=\mathrm{wrecs}\left(R,A,G\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢R=R$$
2		eqid	$$⊢A=A$$
3		wrecseq123	$$⊢\left(R=R\wedge A=A\wedge F=G\right)\to \mathrm{wrecs}\left(R,A,F\right)=\mathrm{wrecs}\left(R,A,G\right)$$
4	1 2 3	mp3an12	$$⊢F=G\to \mathrm{wrecs}\left(R,A,F\right)=\mathrm{wrecs}\left(R,A,G\right)$$