Theorem eximi

Description: Inference adding existential quantifier to antecedent and consequent. (Contributed by NM, 10-Jan-1993)

	Ref	Expression
Hypothesis	eximi.1	⊢ ( 𝜑 → 𝜓 )
Assertion	eximi	⊢ ( ∃ 𝑥 𝜑 → ∃ 𝑥 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		eximi.1	⊢ ( 𝜑 → 𝜓 )
2		exim	⊢ ( ∀ 𝑥 ( 𝜑 → 𝜓 ) → ( ∃ 𝑥 𝜑 → ∃ 𝑥 𝜓 ) )
3	2 1	mpg	⊢ ( ∃ 𝑥 𝜑 → ∃ 𝑥 𝜓 )