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Principia mathematica, vol. 1 (of 3)

*90. ON THE ANCESTRAL RELATION.

Project Gutenberg EPUB3 edition Whitehead, Alfred North and Russell, Bertrand
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This proposition shows that if is a hereditary class which contains , then contains all the descendants of 's.
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In the last line of the above proof, the process is as follows. Writing for , (2) becomes , while (3) becomes . Hence, by (2) and (3), Hence, by *90·112, , which is the proposition to be proved.

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Principia mathematica, vol. 1 (of 3), Project Gutenberg eBook #78050

FOOTNOTES: *91. ON POWERS OF A RELATION.