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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(𝜑𝜓))

Proof of Theorem nfimt
StepHypRef Expression
1 simpl 475 . 2 ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥𝜑)
2 simpr 478 . 2 ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥𝜓)
31, 2nfimd 1993 1 ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 385  wnf 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
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