if and only if

• (UK) IPA^(key): /ɪf ən(d) ˈəʊn.li ɪf/
• (US) IPA^(key): /ɪf ən(d) ˈoʊn.li ɪf/

• Audio (Southern England):

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• Audio (US):

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if and only if

1. (logic, mathematics) Is equivalent to; implies and is implied by; is true and false in the same cases as.

   A rectangle is a square if and only if all four of its sides have the same length.

   An integer is even if and only if its square is also even.

2. (by extension, informal) Synonym of if (with added intensity)

   I'll let you go to the concert if and only if you clean your room.

• logical connective

• if
• if and when
• iff
• only if
• when and only when

• ↔, ⇔