Theorem nfimt 1895

Description: Closed form of nfim 1896 and nfimd 1894. (Contributed by BJ, 20-Oct-2021.) Eliminate curried form, former name nfimt2. (Revised by Wolf Lammen, 6-Jul-2022.)

Assertion

Ref	Expression
nfimt	⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑 → 𝜓))

Proof of Theorem nfimt

Step	Hyp	Ref	Expression
1		simpl 482	. 2 ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥𝜑)
2		simpr 484	. 2 ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥𝜓)
3	1, 2	nfimd 1894	1 ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑 → 𝜓))

Syntax hints:   → wi 4   ∧ wa 395  Ⅎwnf 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780  df-nf 1784

This theorem is referenced by:  nfim  1896