Theorem intnanrd 879

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 107	. 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜓)
3	1, 2	nsyl 593	1 ⊢ (𝜑 → ¬ (𝜓 ∧ 𝜒))

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 579  ax-in2 580

This theorem is referenced by:  dcan  880  bianfd  894  frecabcl  6146  frecsuclem  6153  xrrebnd  9250  fzpreddisj  9452  iseqf1olemqk  9888  gcdsupex  11031  gcdsupcl  11032  nndvdslegcd  11039  divgcdnn  11048  sqgcd  11100  coprm  11205