Metamath Proof Explorer

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 
|- ( ( ( ph -> ps ) /\ ( ps -> ph ) ) <-> ( ph <-> ps ) )

Proof

Step Hyp Ref Expression
1 dfbi2 
 |-  ( ( ph <-> ps ) <-> ( ( ph -> ps ) /\ ( ps -> ph ) ) )
2 1 bicomi 
 |-  ( ( ( ph -> ps ) /\ ( ps -> ph ) ) <-> ( ph <-> ps ) )