Axiom ax-mulass 7598

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axmulass 7558. Proofs should normally use mulass 7623 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 7498	. . . 4 class CC
3	1, 2	wcel 1448	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1448	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1448	. . 3 wff C e. CC
8	3, 5, 7	w3a 930	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 7505	. . . . 5 class x.
10	1, 4, 9	co 5706	. . . 4 class ( A x. B )
11	10, 6, 9	co 5706	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5706	. . . 4 class ( B x. C )
13	1, 12, 9	co 5706	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1299	. 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  7623