WITHIN A FEW MINS OF ASSUMING THE CTL POS; A DISTR ZTL ARTCC CTLR CLRS A DA10 TO CLB THROUGH THE ALT OF AN OPPOSITE DIRECTION B737 RESULTING IN A LOSS OF SEPARATION.

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