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Axiom ax-cnre 8778
 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 8754. (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 8703 . . 3
31, 2wcel 1621 . 2
4 vx . . . . . . 7
54cv 1618 . . . . . 6
6 ci 8707 . . . . . . 7
7 vy . . . . . . . 8
87cv 1618 . . . . . . 7
9 cmul 8710 . . . . . . 7
106, 8, 9co 5792 . . . . . 6
11 caddc 8708 . . . . . 6
125, 10, 11co 5792 . . . . 5
131, 12wceq 1619 . . . 4
14 cr 8704 . . . 4
1513, 7, 14wrex 2519 . . 3
1615, 4, 14wrex 2519 . 2
173, 16wi 6 1
 Colors of variables: wff set class This axiom is referenced by:  mulid1  8802  cnre  8804  1re  8805  recex  9368  cju  9710  cnref1o  10316  replim  11566  ipasslem11  21378
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