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	$$⊢\neg \left(\phi \wedge \psi \wedge \chi \right)$$
Assertion	bj-imn3ani	$$⊢\left(\phi \wedge \psi \right)\to \neg \chi$$

Proof

Step	Hyp	Ref	Expression
1		bj-imn3ani.1	$$⊢\neg \left(\phi \wedge \psi \wedge \chi \right)$$
2		df-3an	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\leftrightarrow \left(\left(\phi \wedge \psi \right)\wedge \chi \right)$$
3	1 2	mtbi	$$⊢\neg \left(\left(\phi \wedge \psi \right)\wedge \chi \right)$$
4	3	imnani	$$⊢\left(\phi \wedge \psi \right)\to \neg \chi$$