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Metamath Proof Explorer

Theorem 0expd

Description: Value of zero raised to a positive integer power. (Contributed by Mario Carneiro, 28-May-2016)

		Ref	Expression
	Hypothesis	0exp.1	$⊢ φ \to N \in ℕ$
	Assertion	0expd	$⊢ φ \to 0^{N} = 0$

Step	Hyp	Ref	Expression
1		0exp.1	$⊢ φ \to N \in ℕ$
2		0exp	$⊢ N \in ℕ \to 0^{N} = 0$
3	1 2	syl	$⊢ φ \to 0^{N} = 0$