Theorem bnj1322

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

	Ref	Expression
Assertion	bnj1322	$$⊢A=B\to A\cap B=A$$

Proof

Step	Hyp	Ref	Expression
1		eqimss	$$⊢A=B\to A\subseteq B$$
2		dfss2	$$⊢A\subseteq B\leftrightarrow A\cap B=A$$
3	1 2	sylib	$$⊢A=B\to A\cap B=A$$