Theorem aisfina 46856

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

Hypothesis

Ref	Expression
aisfina.1	⊢ (𝜑 ↔ ⊥)

Assertion

Ref	Expression
aisfina	⊢ ¬ 𝜑

Proof of Theorem aisfina

Step	Hyp	Ref	Expression
1		aisfina.1	. 2 ⊢ (𝜑 ↔ ⊥)
2		nbfal 1554	. 2 ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥))
3	1, 2	mpbir 231	1 ⊢ ¬ 𝜑

Syntax hints:  ¬ wn 3   ↔ wb 206  ⊥wfal 1551

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-tru 1542  df-fal 1552

This theorem is referenced by:  aistbisfiaxb  46877  aisfbistiaxb  46878  aifftbifffaibif  46879  aifftbifffaibifff  46880  atnaiana  46881  dandysum2p2e4  46956