Axiom ax-mulass 7931

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axmulass 7889. Proofs should normally use mulass 7959 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 7826	. . . 4 class CC
3	1, 2	wcel 2159	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2159	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2159	. . 3 wff C e. CC
8	3, 5, 7	w3a 979	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 7833	. . . . 5 class x.
10	1, 4, 9	co 5890	. . . 4 class ( A x. B )
11	10, 6, 9	co 5890	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5890	. . . 4 class ( B x. C )
13	1, 12, 9	co 5890	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1363	. 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  7959