Theorem bnj1071

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
Hypothesis	bnj1071.7	$$⊢D=\mathrm{\omega }\setminus \left\{\varnothing \right\}$$
Assertion	bnj1071	$$⊢n\in D\to \mathrm{E}\mathrm{Fr}n$$

Proof

Step	Hyp	Ref	Expression
1		bnj1071.7	$$⊢D=\mathrm{\omega }\setminus \left\{\varnothing \right\}$$
2	1	bnj923	$$⊢n\in D\to n\in \mathrm{\omega }$$
3		nnord	$$⊢n\in \mathrm{\omega }\to \mathrm{Ord}n$$
4		ordfr	$$⊢\mathrm{Ord}n\to \mathrm{E}\mathrm{Fr}n$$
5	2 3 4	3syl	$$⊢n\in D\to \mathrm{E}\mathrm{Fr}n$$