Theorem intn3an2d 1476

Description: Introduction of a triple conjunct inside a contradiction. (Contributed by FL, 27-Dec-2007.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)

Hypothesis

Ref	Expression
intn3and.1	⊢ (𝜑 → ¬ 𝜓)

Assertion

Ref	Expression
intn3an2d	⊢ (𝜑 → ¬ (𝜒 ∧ 𝜓 ∧ 𝜃))

Proof of Theorem intn3an2d

Step	Hyp	Ref	Expression
1		intn3and.1	. 2 ⊢ (𝜑 → ¬ 𝜓)
2		simp2 1133	. 2 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜃) → 𝜓)
3	1, 2	nsyl 142	1 ⊢ (𝜑 → ¬ (𝜒 ∧ 𝜓 ∧ 𝜃))

Syntax hints:  ¬ wn 3   → wi 4   ∧ w3a 1083

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 209  df-an 399  df-3an 1085

This theorem is referenced by:  iooelexlt  34637  lenelioc  41805  icccncfext  42163  fourierdlem10  42396  fourierdlem104  42489  cznnring  44221