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Metamath Proof Explorer

Theorem relogcld

Description: Closure of the natural logarithm function. (Contributed by Mario Carneiro, 29-May-2016)

		Ref	Expression
	Hypothesis	relogcld.1	$⊢ φ \to A \in ℝ^{+}$
	Assertion	relogcld	$⊢ φ \to \log A \in ℝ$

Step	Hyp	Ref	Expression
1		relogcld.1	$⊢ φ \to A \in ℝ^{+}$
2		relogcl	$⊢ A \in ℝ^{+} \to \log A \in ℝ$
3	1 2	syl	$⊢ φ \to \log A \in ℝ$