Theorem aisfina 43141

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 1551	. 2 ⊢ (¬ 𝜑 ↔ (𝜑 ↔ ⊥))
3	1, 2	mpbir 233	1 ⊢ ¬ 𝜑

Syntax hints:  ¬ wn 3   ↔ wb 208  ⊥wfal 1548

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 209  df-tru 1539  df-fal 1549

This theorem is referenced by:  aistbisfiaxb  43162  aisfbistiaxb  43163  aifftbifffaibif  43164  aifftbifffaibifff  43165  atnaiana  43166  dandysum2p2e4  43241