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

Axiom ax-addcl 9573
Description: Closure law for addition of complex numbers. Axiom 4 of 22 for real and complex numbers, justified by theorem axaddcl 9549. Proofs should normally use addcl 9595 instead, which asserts the same thing but follows our naming conventions for closures. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-addcl

Detailed syntax breakdown of Axiom ax-addcl
StepHypRef Expression
1 cA . . . 4
2 cc 9511 . . . 4
31, 2wcel 1818 . . 3
4 cB . . . 4
54, 2wcel 1818 . . 3
63, 5wa 369 . 2
7 caddc 9516 . . . 4
81, 4, 7co 6296 . . 3
98, 2wcel 1818 . 2
106, 9wi 4 1
Colors of variables: wff setvar class
This axiom is referenced by:  addcl  9595
  Copyright terms: Public domain W3C validator