Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ax-mulass | Unicode version |
Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axmulass 7674. Proofs should normally use mulass 7744 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.) |
Ref | Expression |
---|---|
ax-mulass |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . . 4 | |
2 | cc 7611 | . . . 4 | |
3 | 1, 2 | wcel 1480 | . . 3 |
4 | cB | . . . 4 | |
5 | 4, 2 | wcel 1480 | . . 3 |
6 | cC | . . . 4 | |
7 | 6, 2 | wcel 1480 | . . 3 |
8 | 3, 5, 7 | w3a 962 | . 2 |
9 | cmul 7618 | . . . . 5 | |
10 | 1, 4, 9 | co 5767 | . . . 4 |
11 | 10, 6, 9 | co 5767 | . . 3 |
12 | 4, 6, 9 | co 5767 | . . . 4 |
13 | 1, 12, 9 | co 5767 | . . 3 |
14 | 11, 13 | wceq 1331 | . 2 |
15 | 8, 14 | wi 4 | 1 |
Colors of variables: wff set class |
This axiom is referenced by: mulass 7744 |
Copyright terms: Public domain | W3C validator |