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Theorem intnanrd 898
Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 10-Jul-2005.)
Hypothesis
Ref Expression
intnand.1 (𝜑 → ¬ 𝜓)
Assertion
Ref Expression
intnanrd (𝜑 → ¬ (𝜓𝜒))

Proof of Theorem intnanrd
StepHypRef Expression
1 intnand.1 . 2 (𝜑 → ¬ 𝜓)
2 simpl 108 . 2 ((𝜓𝜒) → 𝜓)
31, 2nsyl 600 1 (𝜑 → ¬ (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-in1 586  ax-in2 587
This theorem is referenced by:  dcan  899  bianfd  913  frecabcl  6248  frecsuclem  6255  xrrebnd  9489  fzpreddisj  9738  iseqf1olemqk  10154  gcdsupex  11488  gcdsupcl  11489  nndvdslegcd  11496  divgcdnn  11505  sqgcd  11557  coprm  11662  ctiunctlemudc  11787
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