Preserve conditional formatting on cut-paste

I managed to find one solution, I recorded this macro:

Sub FomattingRules()
'
' FomattingRules Macro
'
' Keyboard Shortcut: Ctrl+e
'
    Cells.Select
    Cells.FormatConditions.Delete

    Selection.FormatConditions.Add Type:=xlExpression, Formula1:= _
        "=MOD(ROW(),2)=0"
    Selection.FormatConditions(Selection.FormatConditions.Count).SetFirstPriority
    With Selection.FormatConditions(1).Interior
        .PatternColorIndex = xlAutomatic
        .ThemeColor = xlThemeColorAccent3
        .TintAndShade = 0.599963377788629
    End With
    Selection.FormatConditions(1).StopIfTrue = False
End Sub

Technically this works but I'd rather find a solution that doesn't require me to press ctrl+e every so often. But it's better than resetting the rules by hand, I guess.