Theorem bj-19.21bit 37177

Description: Closed form of 19.21bi 2227. (Contributed by BJ, 20-Oct-2019.)

Assertion

Ref	Expression
bj-19.21bit	⊢ ((𝜑 → ∀𝑥𝜓) → (𝜑 → 𝜓))

Proof of Theorem bj-19.21bit

Step	Hyp	Ref	Expression
1		sp 2221	. 2 ⊢ (∀𝑥𝜓 → 𝜓)
2	1	imim2i 17	1 ⊢ ((𝜑 → ∀𝑥𝜓) → (𝜑 → 𝜓))

Syntax hints:   → wi 4  ∀wal 1561

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-12 2215

This theorem depends on definitions:  df-bi 210  df-ex 1803

This theorem is referenced by:  bj-wnfenf  37209  bj-dfnnf3  37268