Axiom ax-mulass 7351

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axmulass 7311. Proofs should normally use mulass 7376 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 7251	. . . 4 class CC
3	1, 2	wcel 1434	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1434	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1434	. . 3 wff C e. CC
8	3, 5, 7	w3a 920	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 7258	. . . . 5 class x.
10	1, 4, 9	co 5591	. . . 4 class ( A x. B )
11	10, 6, 9	co 5591	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5591	. . . 4 class ( B x. C )
13	1, 12, 9	co 5591	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1285	. 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  7376