Theorem wfis3

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

	Ref	Expression
Hypotheses	wfis3.1	|- R We A
	wfis3.2	|- R Se A
	wfis3.3	|- ( y = z -> ( ph <-> ps ) )
	wfis3.4	|- ( y = B -> ( ph <-> ch ) )
	wfis3.5	|- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
Assertion	wfis3	|- ( B e. A -> ch )

Proof

Step	Hyp	Ref	Expression
1		wfis3.1	|- R We A
2		wfis3.2	|- R Se A
3		wfis3.3	|- ( y = z -> ( ph <-> ps ) )
4		wfis3.4	|- ( y = B -> ( ph <-> ch ) )
5		wfis3.5	|- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
6	1 2 3 5	wfis2	|- ( y e. A -> ph )
7	4 6	vtoclga	|- ( B e. A -> ch )