Theorem aibandbiaiffaiffb

Description: A closed form showing (a implies b and b implies a) same-as (a same-as b). (Contributed by Jarvin Udandy, 3-Sep-2016)

	Ref	Expression
Assertion	aibandbiaiffaiffb	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜓 → 𝜑 ) ) ↔ ( 𝜑 ↔ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		dfbi2	⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ( ( 𝜑 → 𝜓 ) ∧ ( 𝜓 → 𝜑 ) ) )
2	1	bicomi	⊢ ( ( ( 𝜑 → 𝜓 ) ∧ ( 𝜓 → 𝜑 ) ) ↔ ( 𝜑 ↔ 𝜓 ) )