Theorem nfreu

Description: Bound-variable hypothesis builder for restricted unique existence. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfreuw when possible. (Contributed by NM, 30-Oct-2010) (Revised by Mario Carneiro, 8-Oct-2016) (New usage is discouraged.)

	Ref	Expression
Hypotheses	nfreu.1	$$⊢\underset{\_}{Ⅎ}xA$$
	nfreu.2	$$⊢Ⅎx\phi$$
Assertion	nfreu	$$⊢Ⅎx\exists !y\in A\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfreu.1	$$⊢\underset{\_}{Ⅎ}xA$$
2		nfreu.2	$$⊢Ⅎx\phi$$
3		nftru	$$⊢Ⅎy\top$$
4	1	a1i	$$⊢\top \to \underset{\_}{Ⅎ}xA$$
5	2	a1i	$$⊢\top \to Ⅎx\phi$$
6	3 4 5	nfreud	$$⊢\top \to Ⅎx\exists !y\in A\phi$$
7	6	mptru	$$⊢Ⅎx\exists !y\in A\phi$$