Theorem exa1 1870

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 1867	1 ⊢ (∃𝑥𝜑 → ∃𝑥(𝜓 → 𝜑))

This proof depends on syntax axioms:   → wi 4  ∃wex 1811

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841

This proof depends on definitions:  df-bi 210  df-ex 1812

This theorem is used by:  19.35  1909  bj-exa1i  37592