Theorem bj-19.23bit 37686

Description: Closed form of 19.23bi 2227. (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 2217	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
2	1	imim1i 64	1 ⊢ ((∃𝑥𝜑 → 𝜓) → (𝜑 → 𝜓))

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  ax-5 1942  ax-6 1999  ax-7 2040  ax-12 2212

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

This theorem is used by:  bj-wnfanf  37716  bj-dfnnf3  37776