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Theorem pm3.2ni 878
 Description: Infer negated disjunction of negated premises. (Contributed by NM, 4-Apr-1995.)
Hypotheses
Ref Expression
pm3.2ni.1 ¬ 𝜑
pm3.2ni.2 ¬ 𝜓
Assertion
Ref Expression
pm3.2ni ¬ (𝜑𝜓)

Proof of Theorem pm3.2ni
StepHypRef Expression
1 pm3.2ni.1 . 2 ¬ 𝜑
2 id 22 . . 3 (𝜑𝜑)
3 pm3.2ni.2 . . . 4 ¬ 𝜓
43pm2.21i 119 . . 3 (𝜓𝜑)
52, 4jaoi 854 . 2 ((𝜑𝜓) → 𝜑)
61, 5mto 200 1 ¬ (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∨ wo 844 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 210  df-or 845 This theorem is referenced by:  snsn0non  6296  canthp1lem2  10067  recgt0ii  11538  xrltnr  12507  pnfnlt  12516  nltmnf  12517  smndex1n0mnd  18073  lhop  24615  2lgslem4  25986  axlowdimlem13  26744  3pm3.2ni  32968  nosgnn0  33190  clsk1indlem4  40603  clsk1indlem1  40604  dandysum2p2e4  43454
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