Theorem rpex 46465

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 11296	. 2 ⊢ ℝ ∈ V
2		rpssre 13133	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5283	1 ⊢ ℝ+ ∈ V

This proof depends on syntax axioms:   ∈ wcel 2144  Vcvv 3450  ℝcr 11204  ℝ⁺crp 13125

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732  ax-sep 5248  ax-cnex 11261  ax-resscn 11262

This proof depends on definitions:  df-bi 210  df-an 402  df-3an 1105  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-rab 3413  df-v 3452  df-ss 3897  df-in 4090  df-rp 13126

This theorem is used by:  ovncvrrp  47681  ovnsubaddlem1  47687  ovncvr2  47728