Axiom ax-mulass 7079

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axmulass 7039. Proofs should normally use mulass 7104 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 6979	. . . 4 class CC
3	1, 2	wcel 1433	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1433	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1433	. . 3 wff C e. CC
8	3, 5, 7	w3a 919	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 6986	. . . . 5 class x.
10	1, 4, 9	co 5532	. . . 4 class ( A x. B )
11	10, 6, 9	co 5532	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5532	. . . 4 class ( B x. C )
13	1, 12, 9	co 5532	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1284	. 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  7104