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Theorem intnanrd 875
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 107 . 2 ((𝜓𝜒) → 𝜓)
31, 2nsyl 591 1 (𝜑 → ¬ (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-in1 577  ax-in2 578
This theorem is referenced by:  dcan  876  bianfd  890  frecabcl  6096  frecsuclem  6103  xrrebnd  9176  fzpreddisj  9378  gcdsupex  10729  gcdsupcl  10730  nndvdslegcd  10737  divgcdnn  10746  sqgcd  10798  coprm  10903
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