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	⊢ ∃ 𝑥 𝜑
Assertion	bj-exa1i	⊢ ∃ 𝑥 ( 𝜓 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		bj-exa1i.1	⊢ ∃ 𝑥 𝜑
2		exa1	⊢ ( ∃ 𝑥 𝜑 → ∃ 𝑥 ( 𝜓 → 𝜑 ) )
3	1 2	ax-mp	⊢ ∃ 𝑥 ( 𝜓 → 𝜑 )