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Metamath Proof Explorer

Theorem abscld

Description: Real closure of absolute value. (Contributed by Mario Carneiro, 29-May-2016)

		Ref	Expression
	Hypothesis	abscld.1	$⊢ φ \to A \in ℂ$
	Assertion	abscld	$⊢ φ \to \|A\| \in ℝ$

Step	Hyp	Ref	Expression
1		abscld.1	$⊢ φ \to A \in ℂ$
2		abscl	$⊢ A \in ℂ \to \|A\| \in ℝ$
3	1 2	syl	$⊢ φ \to \|A\| \in ℝ$