Axiom ax-mulass 7395

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axmulass 7355. Proofs should normally use mulass 7420 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 7295	. . . 4 class CC
3	1, 2	wcel 1436	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1436	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1436	. . 3 wff C e. CC
8	3, 5, 7	w3a 922	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 7302	. . . . 5 class x.
10	1, 4, 9	co 5615	. . . 4 class ( A x. B )
11	10, 6, 9	co 5615	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5615	. . . 4 class ( B x. C )
13	1, 12, 9	co 5615	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1287	. 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  7420