Metamath Proof Explorer


Theorem resqrtcld

Description: The square root of a nonnegative real is a real. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypotheses resqrcld.1 φA
resqrcld.2 φ0A
Assertion resqrtcld φA

Proof

Step Hyp Ref Expression
1 resqrcld.1 φA
2 resqrcld.2 φ0A
3 resqrtcl A0AA
4 1 2 3 syl2anc φA