Theorem rpex 45302

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 11229	. 2 ⊢ ℝ ∈ V
2		rpssre 13025	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5304	1 ⊢ ℝ+ ∈ V

Syntax hints:   ∈ wcel 2107  Vcvv 3464  ℝcr 11137  ℝ⁺crp 13017

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706  ax-sep 5278  ax-cnex 11194  ax-resscn 11195

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-rab 3421  df-v 3466  df-in 3940  df-ss 3950  df-rp 13018

This theorem is referenced by:  ovncvrrp  46524  ovnsubaddlem1  46530  ovncvr2  46571