Theorem opelresi

Description: Ordered pair membership in a restriction. Exercise 13 of TakeutiZaring p. 25. (Contributed by NM, 13-Nov-1995)

	Ref	Expression
Hypothesis	opelresi.1	|- C e. _V
Assertion	opelresi	|- ( <. B , C >. e. ( R |` A ) <-> ( B e. A /\ <. B , C >. e. R ) )

Proof

Step	Hyp	Ref	Expression
1		opelresi.1	|- C e. _V
2		opelres	|- ( C e. _V -> ( <. B , C >. e. ( R |` A ) <-> ( B e. A /\ <. B , C >. e. R ) ) )
3	1 2	ax-mp	|- ( <. B , C >. e. ( R |` A ) <-> ( B e. A /\ <. B , C >. e. R ) )