Theorem bj-imn3ani

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

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

Proof

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