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Axiom ax-cnre 6794
Description: A complex number can be expressed in terms of two reals. Definition 10-1.1(v) of [Gleason] p. 130. Axiom for real and complex numbers, justified by theorem axcnre 6765. For naming consistency, use cnre 6821 for new proofs. (New usage is discouraged.) (Contributed by NM, 9-May-1999.)
Assertion
Ref Expression
ax-cnre  CC  RR  RR  +  _i  x.
Distinct variable group:   ,,

Detailed syntax breakdown of Axiom ax-cnre
StepHypRef Expression
1 cA . . 3
2 cc 6709 . . 3  CC
31, 2wcel 1390 . 2  CC
4 vx . . . . . . 7  setvar
54cv 1241 . . . . . 6
6 ci 6713 . . . . . . 7  _i
7 vy . . . . . . . 8  setvar
87cv 1241 . . . . . . 7
9 cmul 6716 . . . . . . 7  x.
106, 8, 9co 5455 . . . . . 6  _i  x.
11 caddc 6714 . . . . . 6  +
125, 10, 11co 5455 . . . . 5  +  _i  x.
131, 12wceq 1242 . . . 4  +  _i  x.
14 cr 6710 . . . 4  RR
1513, 7, 14wrex 2301 . . 3  RR  +  _i  x.
1615, 4, 14wrex 2301 . 2  RR  RR  +  _i  x.
173, 16wi 4 1  CC  RR  RR  +  _i  x.
Colors of variables: wff set class
This axiom is referenced by:  cnre  6821
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