Theorem rpex 45353

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 11225	. 2 ⊢ ℝ ∈ V
2		rpssre 13021	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5297	1 ⊢ ℝ+ ∈ V

Syntax hints:   ∈ wcel 2109  Vcvv 3464  ℝcr 11133  ℝ⁺crp 13013

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2708  ax-sep 5271  ax-cnex 11190  ax-resscn 11191

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2715  df-cleq 2728  df-clel 2810  df-rab 3421  df-v 3466  df-in 3938  df-ss 3948  df-rp 13014

This theorem is referenced by:  ovncvrrp  46573  ovnsubaddlem1  46579  ovncvr2  46620