Theorem wfis2

Description: Well-Ordered Induction schema, using implicit substitution. (Contributed by Scott Fenton, 29-Jan-2011)

	Ref	Expression
Hypotheses	wfis2.1	|- R We A
	wfis2.2	|- R Se A
	wfis2.3	|- ( y = z -> ( ph <-> ps ) )
	wfis2.4	|- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
Assertion	wfis2	|- ( y e. A -> ph )

Proof

Step	Hyp	Ref	Expression
1		wfis2.1	|- R We A
2		wfis2.2	|- R Se A
3		wfis2.3	|- ( y = z -> ( ph <-> ps ) )
4		wfis2.4	|- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
5	3 4	wfis2g	|- ( ( R We A /\ R Se A ) -> A. y e. A ph )
6	1 2 5	mp2an	|- A. y e. A ph
7	6	rspec	|- ( y e. A -> ph )