Theorem intn3an3d 1477

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
intn3an3d	⊢ (𝜑 → ¬ (𝜒 ∧ 𝜃 ∧ 𝜓))

Proof of Theorem intn3an3d

Step	Hyp	Ref	Expression
1		intn3and.1	. 2 ⊢ (𝜑 → ¬ 𝜓)
2		simp3 1134	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜓) → 𝜓)
3	1, 2	nsyl 142	1 ⊢ (𝜑 → ¬ (𝜒 ∧ 𝜃 ∧ 𝜓))

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:  en3lp  9071  winainflem  10109  ccatalpha  13941  clwwlk  27755  gtnelioc  41758  icccncfext  42163  fourierdlem10  42396