Theorem exa1 1837

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

Assertion

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

Proof of Theorem exa1

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (𝜑 → (𝜓 → 𝜑))
2	1	eximi 1834	1 ⊢ (∃𝑥𝜑 → ∃𝑥(𝜓 → 𝜑))

Syntax hints:   → wi 4  ∃wex 1778

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808

This theorem depends on definitions:  df-bi 207  df-ex 1779

This theorem is referenced by:  19.35  1876