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Mirrors > Home > ILE Home > Th. List > ax-precex | Unicode version |
Description: Existence of reciprocal of positive real number. Axiom for real and complex numbers, justified by theorem axprecex 7688. (Contributed by Jim Kingdon, 6-Feb-2020.) |
Ref | Expression |
---|---|
ax-precex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . . 4 | |
2 | cr 7619 | . . . 4 | |
3 | 1, 2 | wcel 1480 | . . 3 |
4 | cc0 7620 | . . . 4 | |
5 | cltrr 7624 | . . . 4 | |
6 | 4, 1, 5 | wbr 3929 | . . 3 |
7 | 3, 6 | wa 103 | . 2 |
8 | vx | . . . . . 6 | |
9 | 8 | cv 1330 | . . . . 5 |
10 | 4, 9, 5 | wbr 3929 | . . . 4 |
11 | cmul 7625 | . . . . . 6 | |
12 | 1, 9, 11 | co 5774 | . . . . 5 |
13 | c1 7621 | . . . . 5 | |
14 | 12, 13 | wceq 1331 | . . . 4 |
15 | 10, 14 | wa 103 | . . 3 |
16 | 15, 8, 2 | wrex 2417 | . 2 |
17 | 7, 16 | wi 4 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: recexre 8340 recexgt0 8342 |
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