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Theorem intnand 840
Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 10-Jul-2005.)
Hypothesis
Ref Expression
intnand.1 (𝜑 → ¬ 𝜓)
Assertion
Ref Expression
intnand (𝜑 → ¬ (𝜒𝜓))

Proof of Theorem intnand
StepHypRef Expression
1 intnand.1 . 2 (𝜑 → ¬ 𝜓)
2 simpr 103 . 2 ((𝜒𝜓) → 𝜓)
31, 2nsyl 558 1 (𝜑 → ¬ (𝜒𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 100  ax-in1 544  ax-in2 545
This theorem is referenced by:  dcan  842  poxp  5853  cauappcvgprlemladdrl  6755  caucvgprlemladdrl  6776  xrrebnd  8732  fzpreddisj  8933  fzp1nel  8966
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