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Axiom ax-rnegex 6772
Description: Existence of negative of real number. Axiom for real and complex numbers, justified by theorem axrnegex 6743. (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 6690 . . 3 class
31, 2wcel 1390 . 2 wff A
4 vx . . . . . 6 setvar x
54cv 1241 . . . . 5 class x
6 caddc 6694 . . . . 5 class +
71, 5, 6co 5455 . . . 4 class (A + x)
8 cc0 6691 . . . 4 class 0
97, 8wceq 1242 . . 3 wff (A + x) = 0
109, 4, 2wrex 2301 . 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  6805  readdcan  6930  cnegexlem1  6963  cnegexlem2  6964  cnegexlem3  6965  cnegex  6966  renegcl  7048  ltadd2  7192
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