Theorem rpex 45296

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 11244	. 2 ⊢ ℝ ∈ V
2		rpssre 13040	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5328	1 ⊢ ℝ+ ∈ V

Syntax hints:   ∈ wcel 2106  Vcvv 3478  ℝcr 11152  ℝ⁺crp 13032

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-sep 5302  ax-cnex 11209  ax-resscn 11210

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-in 3970  df-ss 3980  df-rp 13033

This theorem is referenced by:  ovncvrrp  46520  ovnsubaddlem1  46526  ovncvr2  46567