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Mirrors > Home > ILE Home > Th. List > ax-addcom | Unicode version |
Description: Addition commutes. Axiom for real and complex numbers, justified by Theorem axaddcom 7819. Proofs should normally use addcom 8043 instead. (New usage is discouraged.) (Contributed by Jim Kingdon, 17-Jan-2020.) |
Ref | Expression |
---|---|
ax-addcom |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . . 4 | |
2 | cc 7759 | . . . 4 | |
3 | 1, 2 | wcel 2141 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 2141 | . . 3 |
6 | 3, 5 | wa 103 | . 2 |
7 | caddc 7764 | . . . 4 | |
8 | 1, 4, 7 | co 5850 | . . 3 |
9 | 4, 1, 7 | co 5850 | . . 3 |
10 | 8, 9 | wceq 1348 | . 2 |
11 | 6, 10 | wi 4 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: addcom 8043 |
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