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Theorem intnanrd 902
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 602 1 (𝜑 → ¬ (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-in1 588  ax-in2 589
This theorem is referenced by:  dcan  903  bianfd  917  frecabcl  6264  frecsuclem  6271  xrrebnd  9570  fzpreddisj  9819  iseqf1olemqk  10235  gcdsupex  11573  gcdsupcl  11574  nndvdslegcd  11581  divgcdnn  11590  sqgcd  11644  coprm  11749  ctiunctlemudc  11877
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