# Proof 7.7

From the projective geometry axioms, prove that two distinct lines have exactly one point in common.

Proof{By Contradiction}: Assume that two distinct lines, and , exist and let them meet at two points and . From Projective Axiom 2, we know that and share exactly one line. However, this goes against our assumption that two distinct lines exist. Therefore, by contradiction, we know that two distinct lines have exactly one point in common.

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