Theorem wfis2g

Description: Well-Ordered Induction Schema, using implicit substitution. (Contributed by Scott Fenton, 11-Feb-2011)

	Ref	Expression
Hypotheses	wfis2g.1	|- ( y = z -> ( ph <-> ps ) )
	wfis2g.2	|- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
Assertion	wfis2g	|- ( ( R We A /\ R Se A ) -> A. y e. A ph )

Proof

Step	Hyp	Ref	Expression
1		wfis2g.1	|- ( y = z -> ( ph <-> ps ) )
2		wfis2g.2	|- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
3		nfv	|- F/ y ps
4	3 1 2	wfis2fg	|- ( ( R We A /\ R Se A ) -> A. y e. A ph )