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Metamath Proof Explorer

Theorem cyclprop

Description: The properties of a cycle: A cycle is a closed path. (Contributed by AV, 31-Jan-2021) (Proof shortened by AV, 30-Oct-2021)

		Ref	Expression
	Assertion	cyclprop	$⊢ F Cycles (G) P \to (F Paths (G) P \land P (0) = P (\|F\|))$

Step	Hyp	Ref	Expression
1		iscycl	$⊢ F Cycles (G) P \leftrightarrow (F Paths (G) P \land P (0) = P (\|F\|))$
2	1	biimpi	$⊢ F Cycles (G) P \to (F Paths (G) P \land P (0) = P (\|F\|))$