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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 7809. (Contributed by NM, 13-Oct-2005.) |
Ref | Expression |
---|---|
ax-pre-mulgt0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . . 4 | |
2 | cr 7733 | . . . 4 | |
3 | 1, 2 | wcel 2128 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 2128 | . . 3 |
6 | 3, 5 | wa 103 | . 2 |
7 | cc0 7734 | . . . . 5 | |
8 | cltrr 7738 | . . . . 5 | |
9 | 7, 1, 8 | wbr 3967 | . . . 4 |
10 | 7, 4, 8 | wbr 3967 | . . . 4 |
11 | 9, 10 | wa 103 | . . 3 |
12 | cmul 7739 | . . . . 5 | |
13 | 1, 4, 12 | co 5826 | . . . 4 |
14 | 7, 13, 8 | wbr 3967 | . . 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 7951 |
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