Theorem bnj1224

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj1224.1	⊢ ¬ ( 𝜃 ∧ 𝜏 ∧ 𝜂 )
Assertion	bnj1224	⊢ ( ( 𝜃 ∧ 𝜏 ) → ¬ 𝜂 )

Proof

Step	Hyp	Ref	Expression
1		bnj1224.1	⊢ ¬ ( 𝜃 ∧ 𝜏 ∧ 𝜂 )
2		df-3an	⊢ ( ( 𝜃 ∧ 𝜏 ∧ 𝜂 ) ↔ ( ( 𝜃 ∧ 𝜏 ) ∧ 𝜂 ) )
3	1 2	mtbi	⊢ ¬ ( ( 𝜃 ∧ 𝜏 ) ∧ 𝜂 )
4	3	imnani	⊢ ( ( 𝜃 ∧ 𝜏 ) → ¬ 𝜂 )