Theorem rpex 46327

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 11284	. 2 ⊢ ℝ ∈ V
2		rpssre 13121	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5284	1 ⊢ ℝ+ ∈ V

This proof depends on syntax axioms:   ∈ wcel 2145  Vcvv 3451  ℝcr 11192  ℝ⁺crp 13113

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 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2733  ax-sep 5249  ax-cnex 11249  ax-resscn 11250

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3414  df-v 3453  df-in 3906  df-ss 3916  df-rp 13114

This theorem is used by:  ovncvrrp  47543  ovnsubaddlem1  47549  ovncvr2  47590