Axiom ax-mulass 7747

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axmulass 7705. Proofs should normally use mulass 7775 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 7642	. . . 4 class CC
3	1, 2	wcel 1481	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1481	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1481	. . 3 wff C e. CC
8	3, 5, 7	w3a 963	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 7649	. . . . 5 class x.
10	1, 4, 9	co 5782	. . . 4 class ( A x. B )
11	10, 6, 9	co 5782	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5782	. . . 4 class ( B x. C )
13	1, 12, 9	co 5782	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1332	. 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  7775