Theorem bj-19.23bit 37357

Description: Closed form of 19.23bi 2230. (Contributed by BJ, 20-Oct-2019.)

Assertion

Ref	Expression
bj-19.23bit	⊢ ((∃𝑥𝜑 → 𝜓) → (𝜑 → 𝜓))

Proof of Theorem bj-19.23bit

Step	Hyp	Ref	Expression
1		19.8a 2220	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
2	1	imim1i 64	1 ⊢ ((∃𝑥𝜑 → 𝜓) → (𝜑 → 𝜓))

This proof depends on syntax axioms:   → wi 4  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-12 2216

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by:  bj-wnfanf  37387  bj-dfnnf3  37447