Axiom ax-mulass 8195

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axmulass 8153. Proofs should normally use mulass 8223 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 8090	. . . 4 class CC
3	1, 2	wcel 2202	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2202	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2202	. . 3 wff C e. CC
8	3, 5, 7	w3a 1005	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 8097	. . . . 5 class x.
10	1, 4, 9	co 6028	. . . 4 class ( A x. B )
11	10, 6, 9	co 6028	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 6028	. . . 4 class ( B x. C )
13	1, 12, 9	co 6028	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1398	. 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  8223