Theorem inegd

Description: Negation introduction rule from natural deduction. (Contributed by Mario Carneiro, 9-Feb-2017)

	Ref	Expression
Hypothesis	inegd.1	$$⊢\left(\phi \wedge \psi \right)\to \perp$$
Assertion	inegd	$$⊢\phi \to \neg \psi$$

Proof

Step	Hyp	Ref	Expression
1		inegd.1	$$⊢\left(\phi \wedge \psi \right)\to \perp$$
2	1	ex	$$⊢\phi \to \left(\psi \to \perp \right)$$
3		dfnot	$$⊢\neg \psi \leftrightarrow \left(\psi \to \perp \right)$$
4	2 3	sylibr	$$⊢\phi \to \neg \psi$$