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Theorem pm3.2ni 895
 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 115 . . 3 (𝜓𝜑)
52, 4jaoi 393 . 2 ((𝜑𝜓) → 𝜑)
61, 5mto 187 1 ¬ (𝜑𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∨ wo 382 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 196  df-or 384 This theorem is referenced by:  snsn0non  5763  canthp1lem2  9354  recgt0ii  10808  xrltnr  11829  pnfnlt  11838  nltmnf  11839  lhop  23583  2lgslem4  24931  axlowdimlem13  25634  3pm3.2ni  30849  nosgnn0  31055  clsk1indlem4  37362  clsk1indlem1  37363  dandysum2p2e4  39814
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