Theorem dfss3

Description: Alternate definition of subclass relationship. (Contributed by NM, 14-Oct-1999)

	Ref	Expression
Assertion	dfss3	$$⊢A\subseteq B\leftrightarrow \forall x\in Ax\in B$$

Proof

Step	Hyp	Ref	Expression
1		df-ss	$$⊢A\subseteq B\leftrightarrow \forall x\left(x\in A\to x\in B\right)$$
2		df-ral	$$⊢\forall x\in Ax\in B\leftrightarrow \forall x\left(x\in A\to x\in B\right)$$
3	1 2	bitr4i	$$⊢A\subseteq B\leftrightarrow \forall x\in Ax\in B$$