MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-pre-mulgt0 Unicode version

Axiom ax-pre-mulgt0 9305
Description: The product of two positive reals is positive. Axiom 21 of 22 for real and complex numbers, justified by theorem axpre-mulgt0 9281. Normally new proofs would use axmulgt0 9395. (New usage is discouraged.) (Contributed by NM, 13-Oct-2005.)
Assertion
Ref Expression
ax-pre-mulgt0

Detailed syntax breakdown of Axiom ax-pre-mulgt0
StepHypRef Expression
1 cA . . . 4
2 cr 9227 . . . 4
31, 2wcel 1749 . . 3
4 cB . . . 4
54, 2wcel 1749 . . 3
63, 5wa 362 . 2
7 cc0 9228 . . . . 5
8 cltrr 9232 . . . . 5
97, 1, 8wbr 4267 . . . 4
107, 4, 8wbr 4267 . . . 4
119, 10wa 362 . . 3
12 cmul 9233 . . . . 5
131, 4, 12co 6061 . . . 4
147, 13, 8wbr 4267 . . 3
1511, 14wi 4 . 2
166, 15wi 4 1
Colors of variables: wff setvar class
This axiom is referenced by:  axmulgt0  9395
  Copyright terms: Public domain W3C validator