Axiom ax-mulass 6987

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axmulass 6947. Proofs should normally use mulass 7012 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 6887	. . . 4 class CC
3	1, 2	wcel 1393	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1393	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1393	. . 3 wff C e. CC
8	3, 5, 7	w3a 885	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 6894	. . . . 5 class x.
10	1, 4, 9	co 5512	. . . 4 class ( A x. B )
11	10, 6, 9	co 5512	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5512	. . . 4 class ( B x. C )
13	1, 12, 9	co 5512	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1243	. 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  7012