Theorem conimpfalt 44300

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

Hypotheses

Ref	Expression
conimpfalt.1	⊢ 𝜑
conimpfalt.2	⊢ ¬ 𝜓
conimpfalt.3	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
conimpfalt	⊢ (𝜑 ↔ ⊥)

Proof of Theorem conimpfalt

Step	Hyp	Ref	Expression
1		conimpfalt.3	. 2 ⊢ (𝜑 → 𝜓)
2		conimpfalt.2	. 2 ⊢ ¬ 𝜓
3	1, 2	aibnbaif 44289	1 ⊢ (𝜑 ↔ ⊥)

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 205  ⊥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 206  df-tru 1542  df-fal 1552

This theorem is referenced by: (None)