![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > ax-pre-mulgt0 | Unicode version |
Description: The product of two positive reals is positive. Axiom for real and complex numbers, justified by theorem axpre-mulgt0 6961. (Contributed by NM, 13-Oct-2005.) |
Ref | Expression |
---|---|
ax-pre-mulgt0 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA |
. . . 4
![]() ![]() | |
2 | cr 6888 |
. . . 4
![]() ![]() | |
3 | 1, 2 | wcel 1393 |
. . 3
![]() ![]() ![]() ![]() |
4 | cB |
. . . 4
![]() ![]() | |
5 | 4, 2 | wcel 1393 |
. . 3
![]() ![]() ![]() ![]() |
6 | 3, 5 | wa 97 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | cc0 6889 |
. . . . 5
![]() ![]() | |
8 | cltrr 6893 |
. . . . 5
![]() ![]() | |
9 | 7, 1, 8 | wbr 3764 |
. . . 4
![]() ![]() ![]() ![]() |
10 | 7, 4, 8 | wbr 3764 |
. . . 4
![]() ![]() ![]() ![]() |
11 | 9, 10 | wa 97 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | cmul 6894 |
. . . . 5
![]() ![]() | |
13 | 1, 4, 12 | co 5512 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() |
14 | 7, 13, 8 | wbr 3764 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 11, 14 | wi 4 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 6, 15 | wi 4 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
This axiom is referenced by: axmulgt0 7091 |
Copyright terms: Public domain | W3C validator |