Axiom ax-mulass 8125

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axmulass 8083. Proofs should normally use mulass 8153 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 8020	. . . 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 8027	. . . . 5 class x.
10	1, 4, 9	co 6013	. . . 4 class ( A x. B )
11	10, 6, 9	co 6013	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 6013	. . . 4 class ( B x. C )
13	1, 12, 9	co 6013	. . 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  8153