Theorem wfr2OLD

Description: Obsolete version of wfr2 as of 18-Nov-2024. (New usage is discouraged.) (Proof modification is discouraged.) (Contributed by Scott Fenton, 18-Apr-2011) (Revised by Mario Carneiro, 26-Jun-2015)

	Ref	Expression
Hypotheses	wfr2OLD.1	|- R We A
	wfr2OLD.2	|- R Se A
	wfr2OLD.3	|- F = wrecs ( R , A , G )
Assertion	wfr2OLD	|- ( X e. A -> ( F ` X ) = ( G ` ( F |` Pred ( R , A , X ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		wfr2OLD.1	|- R We A
2		wfr2OLD.2	|- R Se A
3		wfr2OLD.3	|- F = wrecs ( R , A , G )
4		eqid	|- ( F u. { <. x , ( G ` ( F |` Pred ( R , A , x ) ) ) >. } ) = ( F u. { <. x , ( G ` ( F |` Pred ( R , A , x ) ) ) >. } )
5	1 2 3 4	wfrlem16OLD	|- dom F = A
6	5	eleq2i	|- ( X e. dom F <-> X e. A )
7	1 2 3	wfr2aOLD	|- ( X e. dom F -> ( F ` X ) = ( G ` ( F |` Pred ( R , A , X ) ) ) )
8	6 7	sylbir	|- ( X e. A -> ( F ` X ) = ( G ` ( F |` Pred ( R , A , X ) ) ) )