‏ 1 Corinthians 7:12-14

To the rest I speak, not the Lord. On the circumstances that follow, the Lord has not directly spoken, as he did on divorce; hence, Paul speaks by inspiration.

If any brother hath a wife that believeth not, etc. If either husband or wife is converted, and the other is not, they must not on this account forsake the unbelieving helpmeet, provided he or she is pleased to remain.
For the unbelieving husband is sanctified by the wife, etc. This passage has been much debated, and little understood. The unbelieving husband or wife is not made personally holy, not do the children of believers have personal holiness transmitted to them by virtue of birth relation. Sanctification, then, means something besides personal holiness. To sanctify is to separate to a sacred use, or relation (Ex 20:8 28:38). Food is "sanctified by the word of God and prayer" (1Ti 4:4,5). Here Paul uses the term to denote that one Christian member of a household brings a sanctifying influence to it, so that all the members are to be regarded as separated in part from the great, ungodly, unclean world. Nehemiah commanded Jews to part from heathen wives on the ground that they were ceremonially unclean (Ne 13:23-27). Paul insists, rather, that the believer cleanses the other, and that the unbelieving partner, or the children, are rendered ceremonially clean.

But now are they holy. Brought into such a sacred relation that the unbelieiving partners are under the power of sacred influences, and not to be counted as sources of defilement.
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