Theorem wfr1OLD

Description: Obsolete version of wfr1 as of 18-Nov-2024. (New usage is discouraged.) (Proof modification is discouraged.) (Contributed by Scott Fenton, 22-Apr-2011) (Revised by Mario Carneiro, 26-Jun-2015)

	Ref	Expression
Hypotheses	wfr1OLD.1	$$⊢R\mathrm{We}A$$
	wfr1OLD.2	$$⊢R\mathrm{Se}A$$
	wfr1OLD.3	$$⊢F=\mathrm{wrecs}\left(R,A,G\right)$$
Assertion	wfr1OLD	$$⊢FFnA$$

Proof

Step	Hyp	Ref	Expression
1		wfr1OLD.1	$$⊢R\mathrm{We}A$$
2		wfr1OLD.2	$$⊢R\mathrm{Se}A$$
3		wfr1OLD.3	$$⊢F=\mathrm{wrecs}\left(R,A,G\right)$$
4	1 2 3	wfrfunOLD	$$⊢\mathrm{Fun}F$$
5		eqid	$$⊢F\cup \left\{⟨z,G\left({F\upharpoonright }_{Pred\left(R,A,z\right)}\right)⟩\right\}=F\cup \left\{⟨z,G\left({F\upharpoonright }_{Pred\left(R,A,z\right)}\right)⟩\right\}$$
6	1 2 3 5	wfrlem16OLD	$$⊢\mathrm{dom}F=A$$
7		df-fn	$$⊢FFnA\leftrightarrow \left(\mathrm{Fun}F\wedge \mathrm{dom}F=A\right)$$
8	4 6 7	mpbir2an	$$⊢FFnA$$