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Axiom ax-pre-mulgt0 6780
Description: The product of two positive reals is positive. Axiom for real and complex numbers, justified by theorem axpre-mulgt0 6751. (Contributed by NM, 13-Oct-2005.)
Assertion
Ref Expression
ax-pre-mulgt0  RR  RR  0  <RR  0  <RR  0  <RR  x.

Detailed syntax breakdown of Axiom ax-pre-mulgt0
StepHypRef Expression
1 cA . . . 4
2 cr 6690 . . . 4  RR
31, 2wcel 1390 . . 3  RR
4 cB . . . 4
54, 2wcel 1390 . . 3  RR
63, 5wa 97 . 2  RR  RR
7 cc0 6691 . . . . 5  0
8 cltrr 6695 . . . . 5  <RR
97, 1, 8wbr 3755 . . . 4  0  <RR
107, 4, 8wbr 3755 . . . 4  0  <RR
119, 10wa 97 . . 3 
0  <RR  0  <RR
12 cmul 6696 . . . . 5  x.
131, 4, 12co 5455 . . . 4  x.
147, 13, 8wbr 3755 . . 3  0  <RR  x.
1511, 14wi 4 . 2  0  <RR  0  <RR  0  <RR  x.
166, 15wi 4 1  RR  RR  0  <RR  0  <RR  0  <RR  x.
Colors of variables: wff set class
This axiom is referenced by:  axmulgt0  6868
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