Use of reactive dyes for dyeing hair

A cosmetic composition, comprising at least one hair dyeing assistant and one or more dyes of the formula I:

• wherein
• a is 1 or 2,
• b is 0 or 1,
• Y is vinyl or a radical of the formula C2H4Q, where Q is an alkali-detachable group,
• L3 is a direct bond or a bridge member of the formula CO—NH—M1, where M1 is C2-C6-alkylene with or without interruption by 1 or 2 unadjacent oxygen atoms, imino or C1-C4-alkylimino groups,
• A1 is hydroxysulfonyl or a radical of the formula SO2Y,
• A2 is hydrogen, hydroxysulfonyl, methoxy, chlorine, bromine or carboxyl,
• W is either in case 1) the radical of a coupling component, of a monoazo dye or additionally, when b=0, of a disazo dye, which may each bear further fiber-reactive groups, or
• in case 2) the radical of a chromophore which optionally has further fiber-reactive groups and is derived from an optionally metallized mono- or disazo dye, from a triphendioxazine, from an anthraquinone, from a metallized formazan or from a metallized phthalocyanine,
• L1 is either in case 1) an azo bridge or
• in case 2) a bridge member of the formula O2S—NZ1, OC—NZ1, Z1N—SO2, Z1N—CO, Z1N—CO—NZ2, NZ1 or
• where M2 is a direct bond or methylene, Z1 and Z2 are each independently of the other hydrogen, C1-C6-alkyl or phenyl and X is fluorine, chlorine or bromine, amino, C1-C6-alkylamino with or without interruption by 1 or 2 unadjacent oxygen atoms, imino or C1-C4-alkylimino groups and with or without hydroxyl substitution, N-pyrrolidinyl, N-piperidinyl, N-morpholinyl, N-piperazinyl or N-(C1-C4)-alkylpiperazinyl, or NZ1 or NZ2 each also represent 1,4-piperazinediyl,
• L2 is a radical of the formula
• where Z3, Z4, Z5 and Z6 are each independently of the others hydrogen, C1-C6-alkyl or phenyl, L4 is C2-C8-alkylene or unsubstituted or C1-C4-alkyl-, C1-C4-alkoxy- or hydroxysulfonyl-substituted phenylene, and X is in each case as defined above.