Theorem bj-nfimt2 32026

Description: Uncurried form of bj-nfimt 32025 and closed form of nfim 1813. (Contributed by BJ, 20-Oct-2021.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-nfimt2	⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑 → 𝜓))

Proof of Theorem bj-nfimt2

Step	Hyp	Ref	Expression
1		bj-nfimt 32025	. 2 ⊢ (Ⅎ𝑥𝜑 → (Ⅎ𝑥𝜓 → Ⅎ𝑥(𝜑 → 𝜓)))
2	1	imp 444	1 ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑 → 𝜓))

Syntax hints:   → wi 4   ∧ wa 383  Ⅎwnf 1699

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728

This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696  df-nf 1701

This theorem is referenced by: (None)