Theorem bnj1317

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

	Ref	Expression
Hypothesis	bnj1317.1	$$⊢A=\left\{x|\phi \right\}$$
Assertion	bnj1317	$$⊢y\in A\to \forall xy\in A$$

Proof

Step	Hyp	Ref	Expression
1		bnj1317.1	$$⊢A=\left\{x|\phi \right\}$$
2		hbab1	$$⊢y\in \left\{x|\phi \right\}\to \forall xy\in \left\{x|\phi \right\}$$
3	1 2	hbxfreq	$$⊢y\in A\to \forall xy\in A$$