Theorem bj-alrim2 36696

Description: Uncurried (imported) form of bj-alrim 36695. (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 36695	. 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 1537  Ⅎwnf 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-12 2176

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779  df-nf 1783

This theorem is referenced by: (None)