Theorem exim

Description: Theorem 19.22 of Margaris p. 90. (Contributed by NM, 10-Jan-1993) (Proof shortened by Wolf Lammen, 4-Jul-2014)

	Ref	Expression
Assertion	exim	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( ∃ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) )

Proof

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