Theorem elin2d

Description: Elementhood in the first set of an intersection - deduction version. (Contributed by Thierry Arnoux, 3-May-2020)

	Ref	Expression
Hypothesis	elin1d.1	$$⊢\phi \to X\in \left(A\cap B\right)$$
Assertion	elin2d	$$⊢\phi \to X\in B$$

Proof

Step	Hyp	Ref	Expression
1		elin1d.1	$$⊢\phi \to X\in \left(A\cap B\right)$$
2		elinel2	$$⊢X\in \left(A\cap B\right)\to X\in B$$
3	1 2	syl	$$⊢\phi \to X\in B$$