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Metamath Proof Explorer

Theorem inegd

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

		Ref	Expression
	Hypothesis	inegd.1	$⊢ (φ \land ψ) \to ⊥$
	Assertion	inegd	$⊢ φ \to \neg ψ$

Step	Hyp	Ref	Expression
1		inegd.1	$⊢ (φ \land ψ) \to ⊥$
2	1	ex	$⊢ φ \to (ψ \to ⊥)$
3		dfnot	$⊢ \neg ψ \leftrightarrow (ψ \to ⊥)$
4	2 3	sylibr	$⊢ φ \to \neg ψ$