Theorem relogcld

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

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

Proof

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