Axiom ax-mulass 7723

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axmulass 7681. Proofs should normally use mulass 7751 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 7618	. . . 4 class CC
3	1, 2	wcel 1480	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1480	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1480	. . 3 wff C e. CC
8	3, 5, 7	w3a 962	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 7625	. . . . 5 class x.
10	1, 4, 9	co 5774	. . . 4 class ( A x. B )
11	10, 6, 9	co 5774	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5774	. . . 4 class ( B x. C )
13	1, 12, 9	co 5774	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1331	. 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  7751