13 Grk “slaves, nor did we …” Because of the length and complexity of the Greek sentence, οὐδέ (oude) was translated as “But … even” and a new sentence started in the translation at the beginning of v. 5.
14 Or “we did not cave in to their demands.”
15 Grk “even for an hour” (an idiom for a very short period of time).
16 In order that the truth of the gospel would remain with you. Paul evidently viewed the demands of the so-called “false brothers” as a departure from the truth contained in the gospel he preached. This was a very serious charge (see Gal 1:8).

In other versions

to them we did not yield in submission even for a moment, so that the truth of the gospel might be preserved for you.

We did not give in to them for a moment, so that the truth of the gospel might be preserved for you.

But we did not give up and submit to these people for even a moment, so that the truth of the gospel would be preserved for you.

But we refused to give in to them for a single moment. We wanted to preserve the truth of the gospel message for you.

to whom not even for an hour did we yield in subjection, in order that the truth of the gospel might remain continually with you.

To whom we gave place by subjection, no, not for an hour; that the truth of the gospel might continue with you.

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