Axiom ax-mulass 8027

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axmulass 7985. Proofs should normally use mulass 8055 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)

Assertion

Ref	Expression
ax-mulass	|- ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A x. B ) x. C ) = ( A x. ( B x. C ) ) )

Detailed syntax breakdown of Axiom ax-mulass

Step	Hyp	Ref	Expression
1		cA	. . . 4 class A
2		cc 7922	. . . 4 class CC
3	1, 2	wcel 2175	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2175	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2175	. . 3 wff C e. CC
8	3, 5, 7	w3a 980	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 7929	. . . . 5 class x.
10	1, 4, 9	co 5943	. . . 4 class ( A x. B )
11	10, 6, 9	co 5943	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5943	. . . 4 class ( B x. C )
13	1, 12, 9	co 5943	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1372	. 2 wff ( ( A x. B ) x. C ) = ( A x. ( B x. C ) )
15	8, 14	wi 4	1 wff ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A x. B ) x. C ) = ( A x. ( B x. C ) ) )

This axiom is referenced by:  mulass  8055