Metamath Proof Explorer


Theorem frpoins2g

Description: Well-Founded Induction schema, using implicit substitution. (Contributed by Scott Fenton, 24-Aug-2022)

Ref Expression
Hypotheses frpoins2g.1
|- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
frpoins2g.3
|- ( y = z -> ( ph <-> ps ) )
Assertion frpoins2g
|- ( ( R Fr A /\ R Po A /\ R Se A ) -> A. y e. A ph )

Proof

Step Hyp Ref Expression
1 frpoins2g.1
 |-  ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
2 frpoins2g.3
 |-  ( y = z -> ( ph <-> ps ) )
3 nfv
 |-  F/ y ps
4 1 3 2 frpoins2fg
 |-  ( ( R Fr A /\ R Po A /\ R Se A ) -> A. y e. A ph )