MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-cnre Unicode version

Axiom ax-cnre 9234
Description: A complex number can be expressed in terms of two reals. Definition 10-1.1(v) of [Gleason] p. 130. Axiom 17 of 22 for real and complex numbers, justified by theorem axcnre 9210. For naming consistency, use cnre 9261 for new proofs. (New usage is discouraged.) (Contributed by NM, 9-May-1999.)
Assertion
Ref Expression
ax-cnre
Distinct variable group:   , ,

Detailed syntax breakdown of Axiom ax-cnre
StepHypRef Expression
1 cA . . 3
2 cc 9159 . . 3
31, 2wcel 1732 . 2
4 vx . . . . . . 7
54cv 1669 . . . . . 6
6 ci 9163 . . . . . . 7
7 vy . . . . . . . 8
87cv 1669 . . . . . . 7
9 cmul 9166 . . . . . . 7
106, 8, 9co 6103 . . . . . 6
11 caddc 9164 . . . . . 6
125, 10, 11co 6103 . . . . 5
131, 12wceq 1670 . . . 4
14 cr 9160 . . . 4
1513, 7, 14wrex 2760 . . 3
1615, 4, 14wrex 2760 . 2
173, 16wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  cnre  9261
  Copyright terms: Public domain W3C validator