Recall our original definition of enthalpy:
H = E + PV
Then for a change in enthalpy:
DH = D E + D(PV)
If we set P constant, then:
             DH = D E + P D V
Since
     qp = DE + PDV
Then
  DH = qp

The change in enthalpy, D H, is then equal to the heat transferred at constant pressure, qp.
Enthalpy = Heat Transferred