Theorem intn3an3d 1512

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 1156	. 2 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜓) → 𝜓)
3	1, 2	nsyl 141	1 ⊢ (𝜑 → ¬ (𝜒 ∧ 𝜃 ∧ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∧ w3a 1103

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105

This theorem is used by:  frxp2  8149  frxp3  8156  en3lp  9593  winainflem  10696  ccatalpha  14652  psdmul  22366  clwwlk  30371  nlimsuc  44208  gtnelioc  46248  icccncfext  46642  fourierdlem10  46872