Theorem bj-19.23bit 36091

Description: Closed form of 19.23bi 2177. (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 2167	. 2 ⊢ (𝜑 → ∃𝑥𝜑)
2	1	imim1i 63	1 ⊢ ((∃𝑥𝜑 → 𝜓) → (𝜑 → 𝜓))

Syntax hints:   → wi 4  ∃wex 1774

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-12 2164

This theorem depends on definitions:  df-bi 206  df-ex 1775

This theorem is referenced by:  bj-wnfanf  36119  bj-dfnnf3  36157