Theorem rpex 45882

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 11157	. 2 ⊢ ℝ ∈ V
2		rpssre 12994	. 2 ⊢ ℝ+ ⊆ ℝ
3	1, 2	ssexi 5275	1 ⊢ ℝ+ ∈ V

Syntax hints:   ∈ wcel 2141  Vcvv 3453  ℝcr 11065  ℝ⁺crp 12986

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733  ax-sep 5243  ax-cnex 11122  ax-resscn 11123

This theorem depends on definitions:  df-bi 209  df-an 400  df-3an 1099  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-rab 3414  df-v 3455  df-in 3909  df-ss 3919  df-rp 12987

This theorem is referenced by:  ovncvrrp  47098  ovnsubaddlem1  47104  ovncvr2  47145