Theorem conimpfalt

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

	Ref	Expression
Hypotheses	conimpfalt.1	⊢ 𝜑
	conimpfalt.2	⊢ ¬ 𝜓
	conimpfalt.3	⊢ ( 𝜑 → 𝜓 )
Assertion	conimpfalt	⊢ ( 𝜑 ↔ ⊥ )

Proof

Step	Hyp	Ref	Expression
1		conimpfalt.1	⊢ 𝜑
2		conimpfalt.2	⊢ ¬ 𝜓
3		conimpfalt.3	⊢ ( 𝜑 → 𝜓 )
4	3 2	aibnbaif	⊢ ( 𝜑 ↔ ⊥ )