Basic mate: K+2B vs K, error or am I dumb?

On the sixth move the mentor wants me to move Bf4, a move I discounted because it leaves the light square bishop hanging after Kh4. On the next step the mentor says that:

"Note that 6...Kh4 7.Bf5 would leave the Black king right where White wants it."

I don't see it. Doesn't 6...Kh4 7.Bf5 leave both bishops hanging? The white king is too far away to save either of them. Here's a screenshot:

Wouldn't Kh4 secure a draw in this position? What am I missing?

Kh4 Bf5 then Kh5 is black's only move then white would probably play something like Kf6.. and then Kh4 is black's only move and then you can play Be6 Kh5 (once again only move) Bg3.. and you push the black king neatly up the board to the corner and mate him..

i don't get why you think Kh4 Bf5 leaves both bishops hanging. could you explain that..?

Aah. I think I must have misread Bf5 as Bg5. My bad! Thanks for all the help :)

there you go