Provided that
From 'Vocabulary' part of The ABC Of Plain Words by Sir E Gowers (1951)

This form of introduction of a stipulation is better than provided without the that and much better than providing. The phrase should be reserved for a true stipulation, as in:

He said he would go to the meeting provided that I went with him,

and not used loosely for if as in:

I expect he will come tomorrow, provided that he comes at all.

Sometimes this misuse of provided that creates difficulties for a reader:

Such emoluments can only count as qualifying for pension provided that they cannot be converted into cash.

The use of provided that obscures the meaning of a sentence that would have been clear with if.

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