Metamath Proof Explorer


Axiom ax-mulass

Description: Multiplication of complex numbers is associative. Axiom 10 of 22 for real and complex numbers, justified by Theorem axmulass . Proofs should normally use mulass instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994)

Ref Expression
Assertion ax-mulass ABCABC=ABC

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA classA
1 cc class
2 0 1 wcel wffA
3 cB classB
4 3 1 wcel wffB
5 cC classC
6 5 1 wcel wffC
7 2 4 6 w3a wffABC
8 cmul class×
9 0 3 8 co classAB
10 9 5 8 co classABC
11 3 5 8 co classBC
12 0 11 8 co classABC
13 10 12 wceq wffABC=ABC
14 7 13 wi wffABCABC=ABC