Theorem bnj1152

Description: Technical lemma for bnj69 . This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Assertion	bnj1152	|- ( Y e. _pred ( X , A , R ) <-> ( Y e. A /\ Y R X ) )

Proof

Step	Hyp	Ref	Expression
1		breq1	|- ( y = Y -> ( y R X <-> Y R X ) )
2		df-bnj14	|- _pred ( X , A , R ) = { y e. A | y R X }
3	1 2	elrab2	|- ( Y e. _pred ( X , A , R ) <-> ( Y e. A /\ Y R X ) )