Metamath Proof Explorer


Theorem tfr2ALT

Description: Alternate proof of tfr2 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 tfr2ALT A On F A = G F A

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 2 3 5 wfr2 A On F A = G F Pred E On A
7 predon A On Pred E On A = A
8 7 reseq2d A On F Pred E On A = F A
9 8 fveq2d A On G F Pred E On A = G F A
10 6 9 eqtrd A On F A = G F A