Theorem frins3

Description: Founded Induction schema, using implicit substitution. (Contributed by Scott Fenton, 6-Feb-2011) (Revised by Mario Carneiro, 26-Jun-2015)

	Ref	Expression
Hypotheses	frins3.1	|- R Fr A
	frins3.2	|- R Se A
	frins3.3	|- ( y = z -> ( ph <-> ps ) )
	frins3.4	|- ( y = B -> ( ph <-> ch ) )
	frins3.5	|- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
Assertion	frins3	|- ( B e. A -> ch )

Proof

Step	Hyp	Ref	Expression
1		frins3.1	|- R Fr A
2		frins3.2	|- R Se A
3		frins3.3	|- ( y = z -> ( ph <-> ps ) )
4		frins3.4	|- ( y = B -> ( ph <-> ch ) )
5		frins3.5	|- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) )
6	1 2 3 5	frins2	|- ( y e. A -> ph )
7	4 6	vtoclga	|- ( B e. A -> ch )