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I think your easiest option would be to use the pen tool to add one point to the line at its intersection, and then delete the segment.
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I think your easiest option would be to use the pen tool to add one point to the line at its intersection, and then delete the segment.
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Try the shapebuilder tool.
Select both the crossing linesand then Alt-click what you don't want.
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You can try changing the lines to fills by expanding then try pathfinders - if you need the lines later, just copy and paste in place and make invisible so you can use them later if needed.