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Axiom ax-rnegex 7820
 Description: Existence of negative of real number. Axiom for real and complex numbers, justified by Theorem axrnegex 7778. (Contributed by Eric Schmidt, 21-May-2007.)
Assertion
Ref Expression
ax-rnegex (𝐴 ∈ ℝ → ∃𝑥 ∈ ℝ (𝐴 + 𝑥) = 0)
Distinct variable group:   𝑥,𝐴

Detailed syntax breakdown of Axiom ax-rnegex
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cr 7710 . . 3 class
31, 2wcel 2125 . 2 wff 𝐴 ∈ ℝ
4 vx . . . . . 6 setvar 𝑥
54cv 1331 . . . . 5 class 𝑥
6 caddc 7714 . . . . 5 class +
71, 5, 6co 5814 . . . 4 class (𝐴 + 𝑥)
8 cc0 7711 . . . 4 class 0
97, 8wceq 1332 . . 3 wff (𝐴 + 𝑥) = 0
109, 4, 2wrex 2433 . 2 wff 𝑥 ∈ ℝ (𝐴 + 𝑥) = 0
113, 10wi 4 1 wff (𝐴 ∈ ℝ → ∃𝑥 ∈ ℝ (𝐴 + 𝑥) = 0)
 Colors of variables: wff set class This axiom is referenced by:  0re  7857  readdcan  7994  cnegexlem1  8029  cnegexlem2  8030  cnegexlem3  8031  cnegex  8032  renegcl  8115  ltadd2  8273
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