Theorem bj-alrim2 36677

Description: Uncurried (imported) form of bj-alrim 36676. (Contributed by BJ, 2-May-2019.)

Assertion

Ref	Expression
bj-alrim2	⊢ ((Ⅎ𝑥𝜑 ∧ ∀𝑥(𝜑 → 𝜓)) → (𝜑 → ∀𝑥𝜓))

Proof of Theorem bj-alrim2

Step	Hyp	Ref	Expression
1		bj-alrim 36676	. 2 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓)))
2	1	imp 406	1 ⊢ ((Ⅎ𝑥𝜑 ∧ ∀𝑥(𝜑 → 𝜓)) → (𝜑 → ∀𝑥𝜓))

Syntax hints:   → wi 4   ∧ wa 395  ∀wal 1535  Ⅎwnf 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-12 2175

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-nf 1781

This theorem is referenced by: (None)