Theorem exa1

Description: Add an antecedent in an existentially quantified formula. (Contributed by BJ, 6-Oct-2018)

	Ref	Expression
Assertion	exa1	⊢ ( ∃ 𝑥 𝜑 → ∃ 𝑥 ( 𝜓 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		ax-1	⊢ ( 𝜑 → ( 𝜓 → 𝜑 ) )
2	1	eximi	⊢ ( ∃ 𝑥 𝜑 → ∃ 𝑥 ( 𝜓 → 𝜑 ) )