Theorem rpex 45798

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 11127	. 2 ⊢ ℝ ∈ V
2		rpssre 12948	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5257	1 ⊢ ℝ+ ∈ V

Syntax hints:   ∈ wcel 2119  Vcvv 3432  ℝcr 11035  ℝ⁺crp 12940

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712  ax-sep 5225  ax-cnex 11092  ax-resscn 11093

This theorem depends on definitions:  df-bi 208  df-an 397  df-3an 1094  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-rab 3393  df-v 3434  df-in 3897  df-ss 3907  df-rp 12941

This theorem is referenced by:  ovncvrrp  47014  ovnsubaddlem1  47020  ovncvr2  47061