Theorem bj-alrim2 37360

Description: Uncurried (imported) form of bj-alrim 37359. (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 37359	. 2 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓)))
2	1	imp 412	1 ⊢ ((Ⅎ𝑥𝜑 ∧ ∀𝑥(𝜑 → 𝜓)) → (𝜑 → ∀𝑥𝜓))

This proof depends on syntax axioms:   → wi 4   ∧ wa 401  ∀wal 1568  Ⅎwnf 1816

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-12 2216

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813  df-nf 1817

This theorem is used by: (None)