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Metamath Proof Explorer

Theorem crctprop

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

		Ref	Expression
	Assertion	crctprop	$⊢ F Circuits (G) P \to (F Trails (G) P \land P (0) = P (\|F\|))$

Step	Hyp	Ref	Expression
1		iscrct	$⊢ F Circuits (G) P \leftrightarrow (F Trails (G) P \land P (0) = P (\|F\|))$
2	1	biimpi	$⊢ F Circuits (G) P \to (F Trails (G) P \land P (0) = P (\|F\|))$