ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-addrcl GIF version

Axiom ax-addrcl 6780
Description: Closure law for addition in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axaddrcl 6751. Proofs should normally use readdcl 6805 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-addrcl ((A B ℝ) → (A + B) ℝ)

Detailed syntax breakdown of Axiom ax-addrcl
StepHypRef Expression
1 cA . . . 4 class A
2 cr 6710 . . . 4 class
31, 2wcel 1390 . . 3 wff A
4 cB . . . 4 class B
54, 2wcel 1390 . . 3 wff B
63, 5wa 97 . 2 wff (A B ℝ)
7 caddc 6714 . . . 4 class +
81, 4, 7co 5455 . . 3 class (A + B)
98, 2wcel 1390 . 2 wff (A + B)
106, 9wi 4 1 wff ((A B ℝ) → (A + B) ℝ)
Colors of variables: wff set class
This axiom is referenced by:  readdcl  6805
  Copyright terms: Public domain W3C validator