Theorem rpex 45794

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 11120	. 2 ⊢ ℝ ∈ V
2		rpssre 12941	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5259	1 ⊢ ℝ+ ∈ V

Syntax hints:   ∈ wcel 2114  Vcvv 3430  ℝcr 11028  ℝ⁺crp 12933

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-sep 5231  ax-cnex 11085  ax-resscn 11086

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3391  df-v 3432  df-in 3897  df-ss 3907  df-rp 12934

This theorem is referenced by:  ovncvrrp  47010  ovnsubaddlem1  47016  ovncvr2  47057