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Metamath Proof Explorer

Theorem eximd

Description: Deduction form of Theorem 19.22 of Margaris p. 90, see exim . (Contributed by NM, 29-Jun-1993) (Revised by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	eximd.1	⊢ Ⅎ 𝑥 𝜑
	eximd.2	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
Assertion	eximd	⊢ ( 𝜑 → ( ∃ 𝑥 𝜓 → ∃ 𝑥 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		eximd.1	⊢ Ⅎ 𝑥 𝜑
2		eximd.2	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
3	1	nf5ri	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
4	3 2	eximdh	⊢ ( 𝜑 → ( ∃ 𝑥 𝜓 → ∃ 𝑥 𝜒 ) )