Thanks.  I updated set.mm with your shorter proof, which you can see at 
http://us2.metamath.org/mpeuni/mmrecent.html#thlist
BTW "bi2" was renamed "biimpr" (for better naming consistency) on Aug. 7.

Norm

On Monday, August 17, 2020 at 3:09:40 AM UTC-4, roger witte wrote:
>
> I was just browsing and noticed that the published proof of bianir has has 
> two redundant commutations of logical equivalence.  The shorter proof goes
>
> 1. bi2 .. ⊢ ((ψ ↔ φ) → (φ → ψ))
> 2. impcom .1.  ⊢ ((φ ∧ (ψ ↔ φ)) → ψ)
>
> Regards
> Roger
>

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