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Axiom ax-cnre 6754
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 6725. For naming consistency, use cnre 6781 for new proofs. (New usage is discouraged.) (Contributed by NM, 9-May-1999.)
Assertion
Ref Expression
ax-cnre (A ℂ → x y A = (x + (i · y)))
Distinct variable group:   x,y,A

Detailed syntax breakdown of Axiom ax-cnre
StepHypRef Expression
1 cA . . 3 class A
2 cc 6669 . . 3 class
31, 2wcel 1390 . 2 wff A
4 vx . . . . . . 7 setvar x
54cv 1241 . . . . . 6 class x
6 ci 6673 . . . . . . 7 class i
7 vy . . . . . . . 8 setvar y
87cv 1241 . . . . . . 7 class y
9 cmul 6676 . . . . . . 7 class ·
106, 8, 9co 5455 . . . . . 6 class (i · y)
11 caddc 6674 . . . . . 6 class +
125, 10, 11co 5455 . . . . 5 class (x + (i · y))
131, 12wceq 1242 . . . 4 wff A = (x + (i · y))
14 cr 6670 . . . 4 class
1513, 7, 14wrex 2301 . . 3 wff y A = (x + (i · y))
1615, 4, 14wrex 2301 . 2 wff x y A = (x + (i · y))
173, 16wi 4 1 wff (A ℂ → x y A = (x + (i · y)))
Colors of variables: wff set class
This axiom is referenced by:  cnre  6781
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