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Database REAL AND COMPLEX NUMBERS Construction and axiomatization of real and complex numbers Real and complex number postulates restated as axioms 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 ⊢ A ∈ ℂ ∧ B ∈ ℂ ∧ C ∈ ℂ → A B C = A B C
Detailed syntax breakdown
Step
Hyp
Ref
Expression
0
cA class A
1
cc class ℂ
2
0 1
wcel wff A ∈ ℂ
3
cB class B
4
3 1
wcel wff B ∈ ℂ
5
cC class C
6
5 1
wcel wff C ∈ ℂ
7
2 4 6
w3a wff A ∈ ℂ ∧ B ∈ ℂ ∧ C ∈ ℂ
8
cmul class ×
9
0 3 8
co class A B
10
9 5 8
co class A B C
11
3 5 8
co class B C
12
0 11 8
co class A B C
13
10 12
wceq wff A B C = A B C
14
7 13
wi wff A ∈ ℂ ∧ B ∈ ℂ ∧ C ∈ ℂ → A B C = A B C