How can I get a world's seed in Minecraft Beta 1.7.3?

use re-create button, then go to more options there you would see the seed of map you are playing. I am 100% sure that the button would be in 1.7.3, because I used to recreate maps in 1.7.2

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You can upload the level.dat file to MineAtlas.com.

It allows you to see the seed.