Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > ax-addrcl | Structured version Visualization version Unicode version |
Description: Closure law for addition in the real subfield of complex numbers. Axiom 6 of 23 for real and complex numbers, justified by theorem axaddrcl 9973. Proofs should normally use readdcl 10019 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-addrcl |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . . 4 | |
2 | cr 9935 | . . . 4 | |
3 | 1, 2 | wcel 1990 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 1990 | . . 3 |
6 | 3, 5 | wa 384 | . 2 |
7 | caddc 9939 | . . . 4 | |
8 | 1, 4, 7 | co 6650 | . . 3 |
9 | 8, 2 | wcel 1990 | . 2 |
10 | 6, 9 | wi 4 | 1 |
Colors of variables: wff setvar class |
This axiom is referenced by: readdcl 10019 |
Copyright terms: Public domain | W3C validator |