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Metamath Proof Explorer

Theorem msqgt0i

Description: A nonzero square is positive. Theorem I.20 of Apostol p. 20. (Contributed by NM, 17-Jan-1997) (Revised by Mario Carneiro, 27-May-2016)

		Ref	Expression
	Hypothesis	lt2.1	$⊢ A \in ℝ$
	Assertion	msqgt0i	$⊢ A \neq 0 \to 0 < A A$

Proof

Step	Hyp	Ref	Expression
1		lt2.1	$⊢ A \in ℝ$
2		msqgt0	$⊢ (A \in ℝ \land A \neq 0) \to 0 < A A$
3	1 2	mpan	$⊢ A \neq 0 \to 0 < A A$