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Theorem pm3.2ni 737
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 19 . . 3 (𝜑𝜑)
3 pm3.2ni.2 . . . 4 ¬ 𝜓
43pm2.21i 585 . . 3 (𝜓𝜑)
52, 4jaoi 646 . 2 ((𝜑𝜓) → 𝜑)
61, 5mto 598 1 ¬ (𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  xrltnr  8802  pnfnlt  8809  nltmnf  8810
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