Theorem bnj1213

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

	Ref	Expression
Hypotheses	bnj1213.1	⊢ 𝐴 ⊆ 𝐵
	bnj1213.2	⊢ ( 𝜃 → 𝑥 ∈ 𝐴 )
Assertion	bnj1213	⊢ ( 𝜃 → 𝑥 ∈ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		bnj1213.1	⊢ 𝐴 ⊆ 𝐵
2		bnj1213.2	⊢ ( 𝜃 → 𝑥 ∈ 𝐴 )
3	1 2	sseldi	⊢ ( 𝜃 → 𝑥 ∈ 𝐵 )