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Theorem pm3.2ni 725
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 ¬ (φ ψ)

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 574 . . 3 (ψφ)
52, 4jaoi 635 . 2 ((φ ψ) → φ)
61, 5mto 587 1 ¬ (φ ψ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wo 628
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  xrltnr  8451  pnfnlt  8458  nltmnf  8459
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