Theorem conimpfalt

Description: Assuming a, not b, and a implies b, there exists a proof that a is false.) (Contributed by Jarvin Udandy, 29-Aug-2016)

	Ref	Expression
Hypotheses	conimpfalt.1	$$⊢\phi$$
	conimpfalt.2	$$⊢\neg \psi$$
	conimpfalt.3	$$⊢\phi \to \psi$$
Assertion	conimpfalt	$$⊢\phi \leftrightarrow \perp$$

Proof

Step	Hyp	Ref	Expression
1		conimpfalt.1	$$⊢\phi$$
2		conimpfalt.2	$$⊢\neg \psi$$
3		conimpfalt.3	$$⊢\phi \to \psi$$
4	3 2	aibnbaif	$$⊢\phi \leftrightarrow \perp$$