Theorem rpex 46045

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 11192	. 2 ⊢ ℝ ∈ V
2		rpssre 13025	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5294	1 ⊢ ℝ+ ∈ V

Syntax hints:   ∈ wcel 2143  Vcvv 3455  ℝcr 11100  ℝ⁺crp 13017

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-sep 5258  ax-cnex 11157  ax-resscn 11158

This theorem depends on definitions:  df-bi 210  df-an 401  df-3an 1105  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3417  df-v 3457  df-in 3913  df-ss 3923  df-rp 13018

This theorem is referenced by:  ovncvrrp  47261  ovnsubaddlem1  47267  ovncvr2  47308