Theorem rpex 45472

Description: The positive reals form a set. (Contributed by Glauco Siliprandi, 11-Oct-2020.)

Assertion

Ref	Expression
rpex	⊢ ℝ+ ∈ V

Proof of Theorem rpex

Step	Hyp	Ref	Expression
1		reex 11106	. 2 ⊢ ℝ ∈ V
2		rpssre 12902	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5264	1 ⊢ ℝ+ ∈ V

Syntax hints:   ∈ wcel 2113  Vcvv 3437  ℝcr 11014  ℝ⁺crp 12894

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705  ax-sep 5238  ax-cnex 11071  ax-resscn 11072

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-rab 3397  df-v 3439  df-in 3905  df-ss 3915  df-rp 12895

This theorem is referenced by:  ovncvrrp  46689  ovnsubaddlem1  46695  ovncvr2  46736