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Theorem pm3.2ni 713
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 562 . . 3 (ψφ)
52, 4jaoi 623 . 2 ((φ ψ) → φ)
61, 5mto 575 1 ¬ (φ ψ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wo 616
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 532  ax-in2 533  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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