Theorem bnj96

Description: Technical lemma for bnj150 . 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) (Revised by Mario Carneiro, 6-May-2015) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj96.1	|- F = { <. (/) , _pred ( x , A , R ) >. }
Assertion	bnj96	|- ( ( R _FrSe A /\ x e. A ) -> dom F = 1o )

Proof

Step	Hyp	Ref	Expression
1		bnj96.1	|- F = { <. (/) , _pred ( x , A , R ) >. }
2		bnj93	|- ( ( R _FrSe A /\ x e. A ) -> _pred ( x , A , R ) e. _V )
3		dmsnopg	|- ( _pred ( x , A , R ) e. _V -> dom { <. (/) , _pred ( x , A , R ) >. } = { (/) } )
4	2 3	syl	|- ( ( R _FrSe A /\ x e. A ) -> dom { <. (/) , _pred ( x , A , R ) >. } = { (/) } )
5	1	dmeqi	|- dom F = dom { <. (/) , _pred ( x , A , R ) >. }
6		df1o2	|- 1o = { (/) }
7	4 5 6	3eqtr4g	|- ( ( R _FrSe A /\ x e. A ) -> dom F = 1o )