Theorem exlimimd

Description: Existential elimination rule of natural deduction. (Contributed by ML, 17-Jul-2020)

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

Proof

Step	Hyp	Ref	Expression
1		exlimimd.1	⊢ ( 𝜑 → ∃ 𝑥 𝜓 )
2		exlimimd.2	⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
3	2	imp	⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
4	1 3	exlimddv	⊢ ( 𝜑 → 𝜒 )