Theorem rpex 46631

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 11330	. 2 ⊢ ℝ ∈ V
2		rpssre 13168	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5291	1 ⊢ ℝ+ ∈ V

This proof depends on syntax axioms:   ∈ wcel 2147  Vcvv 3454  ℝcr 11238  ℝ⁺crp 13160

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-sep 5255  ax-cnex 11295  ax-resscn 11296

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-rab 3417  df-v 3456  df-ss 3901  df-in 4094  df-rp 13161

This theorem is used by:  ovncvrrp  47847  ovnsubaddlem1  47853  ovncvr2  47894