Axiom ax-mulass 8113

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axmulass 8071. Proofs should normally use mulass 8141 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 8008	. . . 4 class CC
3	1, 2	wcel 2200	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2200	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2200	. . 3 wff C e. CC
8	3, 5, 7	w3a 1002	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 8015	. . . . 5 class x.
10	1, 4, 9	co 6007	. . . 4 class ( A x. B )
11	10, 6, 9	co 6007	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 6007	. . . 4 class ( B x. C )
13	1, 12, 9	co 6007	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1395	. 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  8141