but for

Short definition from Wiktionary

Preposition

1. 1
   Except, except for; save for; not counting; were it not for; had it not been for.
2. 2
   despite; in spite of

Adjective

1. 1
   Pertaining to a test of causation whereby an agent or action is considered to have caused an event (and therefore to be responsible and/or liable for said event) if, had said agent or action not existed, the event would not have taken place.