How to create a new column that satisfy different "IF" conditions in R?

I have a big set of data that looks like the following:

Name    SNP.x   ILMN.Strand.x   Customer.Strand.x   SNP.y   ILMN.Strand.y   Customer.Strand.y   
exm-rs10128711  [T/C]   BOT BOT [T/C]   BOT BOT
exm-rs10134944  [A/G]   TOP BOT NA  NA  NA  
exm-rs10218696    NA    NA  NA [T/C] BOT TOP
exm-rs10223421  [A/C]   TOP BOT NA  NA  NA

How do I create new columns "SNP","ILMN.Strand","Customer.Strand", whereby:

1. if (SNP.x = SNP.y), then "SNP","ILMN.Strand","Customer.Strand" would be from "SNP.x","ILMN.Strand.x","Customer.Strand.x"

2. if (SNP.x is not equal to SNP.y), and SNP.x is NA (missing value), then the values in the new columns should be taken from "SNP.y","ILMN.Strand.y","Customer.Strand.y"

3. if (SNP.x is not equal to SNP.y), and SNP.y is NA (missing value), then the values in the new columns should be taken from "SNP.x","ILMN.Strand.x","Customer.Strand.x"

Many thanks in advance! :)