An infinitive can have its own subject. The subject of the infinitive is normally introduced by for.

Compare:

• I will be happy to help you. (I will help you.)
• I will be happy for him to help you. (He will help you.)
• My idea was to study medicine. (= I wanted to study medicine.)
• My idea was for him to study medicine. (= I wanted him to study medicine.)

Note that we use object pronouns (e.g. him, them, her etc.) after for.

• It isn't easy for me to let him go. (NOT It isn't easy for I...)

Uses

The structure for + object + infinitive is common after adjectives, nouns and verbs. It is used when we are referring to possibility, necessity or frequency, when we are expressing wishes, suggestions or plans for the future, and when we are giving personal reactions to situations.

• It is important for the meeting to start on time.
• His idea is for us to travel in separate cars.
• I am anxious for the party to be a success.

Instead of the for-structure, a that-clause with should or a subjunctive is often possible.

• It is important that the meeting should start on time.
• I am anxious that the party should be a success.
• His idea is that we should travel in separate cars.