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Theorem pm3.2ni 894
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 114 . . 3 (𝜓𝜑)
52, 4jaoi 392 . 2 ((𝜑𝜓) → 𝜑)
61, 5mto 186 1 ¬ (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 381
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 195  df-or 383
This theorem is referenced by:  snsn0non  5749  canthp1lem2  9331  recgt0ii  10778  xrltnr  11790  pnfnlt  11799  nltmnf  11800  lhop  23500  2lgslem4  24848  axlowdimlem13  25552  3pm3.2ni  30655  nosgnn0  30861  clsk1indlem4  37165  clsk1indlem1  37166  dandysum2p2e4  39618
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