Theorem aisfina

Description: Given a is equivalent to F. , there exists a proof for not a. (Contributed by Jarvin Udandy, 30-Aug-2016)

	Ref	Expression
Hypothesis	aisfina.1	$$⊢\phi \leftrightarrow \perp$$
Assertion	aisfina	$$⊢\neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		aisfina.1	$$⊢\phi \leftrightarrow \perp$$
2		nbfal	$$⊢\neg \phi \leftrightarrow \left(\phi \leftrightarrow \perp \right)$$
3	1 2	mpbir	$$⊢\neg \phi$$