Theorem bj-exa1i

Description: Add an antecedent in an existentially quantified formula. Inference associated with exa1 . (Contributed by BJ, 6-Oct-2018)

	Ref	Expression
Hypothesis	bj-exa1i.1	$$⊢\exists x\phi$$
Assertion	bj-exa1i	$$⊢\exists x\left(\psi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		bj-exa1i.1	$$⊢\exists x\phi$$
2		exa1	$$⊢\exists x\phi \to \exists x\left(\psi \to \phi \right)$$
3	1 2	ax-mp	$$⊢\exists x\left(\psi \to \phi \right)$$