Axiom ax-mulass 8063

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axmulass 8021. Proofs should normally use mulass 8091 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 7958	. . . 4 class CC
3	1, 2	wcel 2178	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2178	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2178	. . 3 wff C e. CC
8	3, 5, 7	w3a 981	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 7965	. . . . 5 class x.
10	1, 4, 9	co 5967	. . . 4 class ( A x. B )
11	10, 6, 9	co 5967	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5967	. . . 4 class ( B x. C )
13	1, 12, 9	co 5967	. . 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  8091