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 → ¬ (𝜓 ∧ 𝜒))

Proof of Theorem intnanrd

Step	Hyp	Ref	Expression
1		intnand.1	. 2 ⊢ (𝜑 → ¬ 𝜓)
2		simpl 108	. 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜓)
3	1, 2	nsyl 600	1 ⊢ (𝜑 → ¬ (𝜓 ∧ 𝜒))

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