Theorem frins2g

Description: Founded Induction schema, using implicit substitution. (Contributed by Scott Fenton, 8-Feb-2011) (Revised by Mario Carneiro, 26-Jun-2015)

	Ref	Expression
Hypotheses	frins2g.1	|- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
	frins2g.3	|- ( y = z -> ( ph <-> ps ) )
Assertion	frins2g	|- ( ( R Fr A /\ R Se A ) -> A. y e. A ph )

Proof

Step	Hyp	Ref	Expression
1		frins2g.1	|- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
2		frins2g.3	|- ( y = z -> ( ph <-> ps ) )
3		nfv	|- F/ y ps
4	1 3 2	frins2fg	|- ( ( R Fr A /\ R Se A ) -> A. y e. A ph )