Histone methyltransferase that specifically methylates 'Lys-4' of histone H3, when part of the SET1 histone methyltransferase (HMT) complex, but not if the neighboring 'Lys-9' residue is already methylated. H3 'Lys-4' methylation represents a specific tag for epigenetic transcriptional activation. L-lysyl(4)-[histone H3] + 3 S-adenosyl-L-methionine = 3 H(+) + N(6),N(6),N(6)-trimethyl-L-lysyl(4)-[histone H3] + 3 S-adenosyl-L-homocysteine Belongs to the class V-like SAM-binding methyltransferase superfamily.