Theorem elin1d

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	elin1d	$$⊢\phi \to X\in A$$

Proof

Step	Hyp	Ref	Expression
1		elin1d.1	$$⊢\phi \to X\in \left(A\cap B\right)$$
2		elinel1	$$⊢X\in \left(A\cap B\right)\to X\in A$$
3	1 2	syl	$$⊢\phi \to X\in A$$