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Theorem nfimt2 1821
Description: Closed form of nfim 1824 and uncurried (imported) form of nfimt 1820. (Contributed by BJ, 20-Oct-2021.)
Assertion
Ref Expression
nfimt2 ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑𝜓))

Proof of Theorem nfimt2
StepHypRef Expression
1 nfimt 1820 . 2 (Ⅎ𝑥𝜑 → (Ⅎ𝑥𝜓 → Ⅎ𝑥(𝜑𝜓)))
21imp 445 1 ((Ⅎ𝑥𝜑 ∧ Ⅎ𝑥𝜓) → Ⅎ𝑥(𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  wnf 1707
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736
This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1704  df-nf 1709
This theorem is referenced by:  nfimd  1822  nfim  1824
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