Theorem bj-19.21bit 37684

Description: Closed form of 19.21bi 2225. (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 2219	. 2 ⊢ (∀𝑥𝜓 → 𝜓)
2	1	imim2i 17	1 ⊢ ((𝜑 → ∀𝑥𝜓) → (𝜑 → 𝜓))

This proof depends on syntax axioms:   → wi 4  ∀wal 1567

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-wnfenf  37716  bj-dfnnf3  37775