Theorem bj-2exim

Description: Closed form of 2eximi . (Contributed by BJ, 6-May-2019)

	Ref	Expression
Assertion	bj-2exim	⊢ ( ∀ 𝑥 ∀ 𝑦 ( 𝜑 → 𝜓 ) → ( ∃ 𝑥 ∃ 𝑦 𝜑 → ∃ 𝑥 ∃ 𝑦 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		exim	⊢ ( ∀ 𝑦 ( 𝜑 → 𝜓 ) → ( ∃ 𝑦 𝜑 → ∃ 𝑦 𝜓 ) )
2	1	aleximi	⊢ ( ∀ 𝑥 ∀ 𝑦 ( 𝜑 → 𝜓 ) → ( ∃ 𝑥 ∃ 𝑦 𝜑 → ∃ 𝑥 ∃ 𝑦 𝜓 ) )