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	⊢ ( 𝜑 → 𝑋 ∈ ( 𝐴 ∩ 𝐵 ) )
Assertion	elin1d	⊢ ( 𝜑 → 𝑋 ∈ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		elin1d.1	⊢ ( 𝜑 → 𝑋 ∈ ( 𝐴 ∩ 𝐵 ) )
2		elinel1	⊢ ( 𝑋 ∈ ( 𝐴 ∩ 𝐵 ) → 𝑋 ∈ 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → 𝑋 ∈ 𝐴 )