Theorem rpex 45947

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 11187	. 2 ⊢ ℝ ∈ V
2		rpssre 13020	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5290	1 ⊢ ℝ+ ∈ V

Syntax hints:   ∈ wcel 2149  Vcvv 3463  ℝcr 11095  ℝ⁺crp 13012

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741  ax-sep 5258  ax-cnex 11152  ax-resscn 11153

This theorem depends on definitions:  df-bi 210  df-an 401  df-3an 1103  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-rab 3424  df-v 3465  df-in 3920  df-ss 3930  df-rp 13013

This theorem is referenced by:  ovncvrrp  47163  ovnsubaddlem1  47169  ovncvr2  47210