MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nfimt Structured version   Visualization version   GIF version

Theorem nfimt 1893
Description: Closed form of nfim 1894 and nfimd 1892. (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(𝜑𝜓))

Proof of Theorem nfimt
StepHypRef Expression
1 simpl 482 . 2 ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥𝜑)
2 simpr 484 . 2 ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥𝜓)
31, 2nfimd 1892 1 ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  wnf 1780
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806
This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777  df-nf 1781
This theorem is referenced by:  nfim  1894
  Copyright terms: Public domain W3C validator