Theorem bj-rcleq

Description: Relative version of dfcleq . (Contributed by BJ, 27-Dec-2023)

	Ref	Expression
Assertion	bj-rcleq	$$⊢V\cap A=V\cap B\leftrightarrow \forall x\in V\left(x\in A\leftrightarrow x\in B\right)$$

Proof

Step	Hyp	Ref	Expression
1		nfcv	$$⊢\underset{\_}{Ⅎ}xA$$
2		nfcv	$$⊢\underset{\_}{Ⅎ}xB$$
3		nfcv	$$⊢\underset{\_}{Ⅎ}xV$$
4	1 2 3	bj-rcleqf	$$⊢V\cap A=V\cap B\leftrightarrow \forall x\in V\left(x\in A\leftrightarrow x\in B\right)$$