Axiom ax-mulass 8028

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axmulass 7986. Proofs should normally use mulass 8056 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 7923	. . . 4 class CC
3	1, 2	wcel 2176	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2176	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2176	. . 3 wff C e. CC
8	3, 5, 7	w3a 981	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 7930	. . . . 5 class x.
10	1, 4, 9	co 5944	. . . 4 class ( A x. B )
11	10, 6, 9	co 5944	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5944	. . . 4 class ( B x. C )
13	1, 12, 9	co 5944	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1373	. 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  8056