Theorem nfimt 1994

Description: Closed form of nfim 1996 and nfimd 1993. (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 475	. 2 ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥𝜑)
2		simpr 478	. 2 ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥𝜓)
3	1, 2	nfimd 1993	1 ⊢ ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑 → 𝜓))

Syntax hints:   → wi 4   ∧ wa 385  Ⅎwnf 1879

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905

This theorem depends on definitions:  df-bi 199  df-an 386  df-ex 1876  df-nf 1880

This theorem is referenced by:  nfimdOLDOLD  1995  nfim  1996