Theorem bnj1230

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj1230.1	$$⊢B=\left\{x\in A|\phi \right\}$$
Assertion	bnj1230	$$⊢y\in B\to \forall xy\in B$$

Proof

Step	Hyp	Ref	Expression
1		bnj1230.1	$$⊢B=\left\{x\in A|\phi \right\}$$
2		nfrab1	$$⊢\underset{\_}{Ⅎ}x\left\{x\in A|\phi \right\}$$
3	1 2	nfcxfr	$$⊢\underset{\_}{Ⅎ}xB$$
4	3	nfcrii	$$⊢y\in B\to \forall xy\in B$$