In more formal styles, if can be omitted and the auxiliary verb placed before the subject.
– If I had been warned → Had I been warned about the situation, I would have made other arrangements.
– If they had not been ordered to → Had they not been ordered to, they would never have entered the building.
If + should/happen to
We use if + should/happen to to suggest that something is rather unlikely to happen, or may just happen by chance.
Should and happen can be used togheter.
– If you (should) happen to pass a pharmacy, could you get me some aspirin?
We use supposing and imagine in place of if. The meaning is similar.
– Supposing/Imagine you won the lottery – what would you do with the money?
If + was/were to
We use if + was/were to to make an event seem more hypothetical. This structure is not used, e.g. believe.
– If they were to find a way of wiping out malaria, milions of lives would be saved.
If + will/would
We use if + will/would to make requests more polite. In this case the auxiliary will/would means ‘be willing to’.
– If you will just bear with us for a few moments, the Minister will answer your questions.
– If you would be kind enough to send your accounts details, we will settle this matter immediately.