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

Axiom ax-mulrcl 6762
Description: Closure law for multiplication in the real subfield of complex numbers. Axiom for real and complex numbers, justified by theorem axmulrcl 6733. Proofs should normally use remulcl 6787 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)
Assertion
Ref Expression
ax-mulrcl ((A B ℝ) → (A · B) ℝ)

Detailed syntax breakdown of Axiom ax-mulrcl
StepHypRef Expression
1 cA . . . 4 class A
2 cr 6690 . . . 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 cmul 6696 . . . 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:  remulcl  6787
  Copyright terms: Public domain W3C validator