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Metamath Proof Explorer

Theorem 2eximi

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

		Ref	Expression
	Hypothesis	eximi.1	$⊢ φ \to ψ$
	Assertion	2eximi	$⊢ \exists x \exists y φ \to \exists x \exists y ψ$

Step	Hyp	Ref	Expression
1		eximi.1	$⊢ φ \to ψ$
2	1	eximi	$⊢ \exists y φ \to \exists y ψ$
3	2	eximi	$⊢ \exists x \exists y φ \to \exists x \exists y ψ$