Theorem bj-imn3ani 34769

Description: Duplication of bnj1224 32781. Three-fold version of imnani 401. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Revised by BJ, 22-Oct-2019.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
bj-imn3ani.1	⊢ ¬ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
bj-imn3ani	⊢ ((𝜑 ∧ 𝜓) → ¬ 𝜒)

Proof of Theorem bj-imn3ani

Step	Hyp	Ref	Expression
1		bj-imn3ani.1	. . 3 ⊢ ¬ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		df-3an 1088	. . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒))
3	1, 2	mtbi 322	. 2 ⊢ ¬ ((𝜑 ∧ 𝜓) ∧ 𝜒)
4	3	imnani 401	1 ⊢ ((𝜑 ∧ 𝜓) → ¬ 𝜒)

Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 396   ∧ w3a 1086

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 206  df-an 397  df-3an 1088

This theorem is referenced by:  bj-inftyexpidisj  35381