Axiom ax-mulass 7982

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axmulass 7940. Proofs should normally use mulass 8010 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 7877	. . . 4 class CC
3	1, 2	wcel 2167	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2167	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2167	. . 3 wff C e. CC
8	3, 5, 7	w3a 980	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 7884	. . . . 5 class x.
10	1, 4, 9	co 5922	. . . 4 class ( A x. B )
11	10, 6, 9	co 5922	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5922	. . . 4 class ( B x. C )
13	1, 12, 9	co 5922	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1364	. 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  8010