Theorem resqcld

Description: Closure of squaring in reals, deduction form. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	resqcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	resqcld	⊢ ( 𝜑 → ( 𝐴 ↑ 2 ) ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		resqcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		resqcl	⊢ ( 𝐴 ∈ ℝ → ( 𝐴 ↑ 2 ) ∈ ℝ )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 ↑ 2 ) ∈ ℝ )