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	⊢ ( 𝜑 ↔ ⊥ )
Assertion	aisfina	⊢ ¬ 𝜑

Proof

Step	Hyp	Ref	Expression
1		aisfina.1	⊢ ( 𝜑 ↔ ⊥ )
2		nbfal	⊢ ( ¬ 𝜑 ↔ ( 𝜑 ↔ ⊥ ) )
3	1 2	mpbir	⊢ ¬ 𝜑