Theorem bnj1361

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

	Ref	Expression
Hypothesis	bnj1361.1	$$⊢\phi \to \forall x\left(x\in A\to x\in B\right)$$
Assertion	bnj1361	$$⊢\phi \to A\subseteq B$$

Proof

Step	Hyp	Ref	Expression
1		bnj1361.1	$$⊢\phi \to \forall x\left(x\in A\to x\in B\right)$$
2		df-ss	$$⊢A\subseteq B\leftrightarrow \forall x\left(x\in A\to x\in B\right)$$
3	1 2	sylibr	$$⊢\phi \to A\subseteq B$$