Theorem 2eximi

Description: Inference adding two existential quantifiers to antecedent and consequent. (Contributed by NM, 3-Feb-2005)

	Ref	Expression
Hypothesis	eximi.1	⊢ ( 𝜑 → 𝜓 )
Assertion	2eximi	⊢ ( ∃ 𝑥 ∃ 𝑦 𝜑 → ∃ 𝑥 ∃ 𝑦 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		eximi.1	⊢ ( 𝜑 → 𝜓 )
2	1	eximi	⊢ ( ∃ 𝑦 𝜑 → ∃ 𝑦 𝜓 )
3	2	eximi	⊢ ( ∃ 𝑥 ∃ 𝑦 𝜑 → ∃ 𝑥 ∃ 𝑦 𝜓 )