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	$$⊢\neg \left(\theta \wedge \tau \wedge \eta \right)$$
Assertion	bnj1224	$$⊢\left(\theta \wedge \tau \right)\to \neg \eta$$

Proof

Step	Hyp	Ref	Expression
1		bnj1224.1	$$⊢\neg \left(\theta \wedge \tau \wedge \eta \right)$$
2		df-3an	$$⊢\left(\theta \wedge \tau \wedge \eta \right)\leftrightarrow \left(\left(\theta \wedge \tau \right)\wedge \eta \right)$$
3	1 2	mtbi	$$⊢\neg \left(\left(\theta \wedge \tau \right)\wedge \eta \right)$$
4	3	imnani	$$⊢\left(\theta \wedge \tau \right)\to \neg \eta$$