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Theorem nfimdOLDOLD 1942
 Description: Obsolete version of nfimd 1940 as of 6-Jul-2022. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) df-nf 1828 changed. (Revised by Wolf Lammen, 18-Sep-2021.) (New usage is discouraged.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
nfimdOLDOLD.1 (𝜑 → Ⅎ𝑥𝜓)
nfimdOLDOLD.2 (𝜑 → Ⅎ𝑥𝜒)
Assertion
Ref Expression
nfimdOLDOLD (𝜑 → Ⅎ𝑥(𝜓𝜒))

Proof of Theorem nfimdOLDOLD
StepHypRef Expression
1 nfimdOLDOLD.1 . 2 (𝜑 → Ⅎ𝑥𝜓)
2 nfimdOLDOLD.2 . 2 (𝜑 → Ⅎ𝑥𝜒)
3 nfimt 1941 . 2 ((Ⅎ𝑥𝜓 ∧ Ⅎ𝑥𝜒) → Ⅎ𝑥(𝜓𝜒))
41, 2, 3syl2anc 579 1 (𝜑 → Ⅎ𝑥(𝜓𝜒))
 Colors of variables: wff setvar class Syntax hints:   → wi 4  Ⅎwnf 1827 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853 This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1824  df-nf 1828 This theorem is referenced by: (None)
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