What specific language in the document indicates that the freeing of slaves is partly for military reasons?

What document are you referring to.

The Emancipation Proclamation was issued on Sept. 22, 1862. It freed slaves in the rebellious states against the union (slave states and southern states). Although it was issued, it didn't immediately free the slaves. They couldn't just leave their slave owner, they may get killed or tortured. SO, When the Civil War started in 1861-1865, Lincoln had prioritized the union over his freeing of the slaves. (He already issued the emancipation in 1861 anyway) So in 1862, thousands of slaves fled the south and rebellious states to join the Northern Army. When slaves joined the northern army in the free northern states, they became a free man and had quarters to live in. Lincoln was then convinced that what he had done in previous years had turned into a military strategy.