Theorem tfr1ALT

Description: Alternate proof of tfr1 using well-ordered recursion. (Contributed by Scott Fenton, 3-Aug-2020) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	tfrALT.1	⊢ 𝐹 = recs ( 𝐺 )
Assertion	tfr1ALT	⊢ 𝐹 Fn On

Proof

Step	Hyp	Ref	Expression
1		tfrALT.1	⊢ 𝐹 = recs ( 𝐺 )
2		epweon	⊢ E We On
3		epse	⊢ E Se On
4		df-recs	⊢ recs ( 𝐺 ) = wrecs ( E , On , 𝐺 )
5	1 4	eqtri	⊢ 𝐹 = wrecs ( E , On , 𝐺 )
6	5	wfr1	⊢ ( ( E We On ∧ E Se On ) → 𝐹 Fn On )
7	2 3 6	mp2an	⊢ 𝐹 Fn On