A condition without si
Instead of an if-clause with si, you can open the sentence with de + infinitive. English has a similar shortcut: Had I known, … instead of If I had known, …. There too the conjunction disappears and the result sounds a little more formal.
From si-clause to short form
Possible and imagined conditions
The simple infinitive replaces both si + present and si + imperfect subjunctive. The main clause tells you which reading is meant: future or present for a real case, conditional for an imagined one.
Same statement, two forms
With si
Si seguimos así, perderemos el cliente.
If we carry on like this, we'll lose the client.
Si fuera cierto, sería muy grave.
If it were true, it would be very serious.
With de + infinitive
De seguir así, perderemos el cliente.
Carry on like this and we'll lose the client.
De ser cierto, sería muy grave.
Were it true, it would be very serious.
Common phrases
De ser así, te devolvemos el dinero.
If that's the case, we'll refund your money.
De no ser por ti, seguiría buscando piso.
If it weren't for you, I'd still be looking for a flat.
De no mediar acuerdo, el caso irá a juicio.
Failing an agreement, the case will go to court.
Typical of the press and official texts.
What did not happen
With de haber + participle you talk about a condition that was not met in the past. The main clause takes the conditional perfect or, if the consequence is in the present, the simple conditional. Pronouns attach to haber: de habérmelo dicho.
De haberlo sabido, no habría venido.
Had I known, I wouldn't have come.
De habérmelo dicho antes, te habría ayudado.
Had you told me sooner, I would have helped you.
De haber aceptado aquel puesto, ahora viviría en Lisboa.
If I had taken that job, I'd be living in Lisbon now.
Past condition, present consequence.
Subject and register
Usually the subject is the same as in the main clause or clear from context. If the infinitive needs a subject of its own, it goes after the infinitive.
De haber salido el tren a su hora, habríamos llegado.
Had the train left on time, we would have made it.
De enterarse la jefa, nos despide a todos.
If the boss finds out, she'll fire the lot of us.