Axiom ax-mulass 7889

Description: Multiplication of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axmulass 7847. Proofs should normally use mulass 7917 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 7784	. . . 4 class CC
3	1, 2	wcel 2146	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2146	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2146	. . 3 wff C e. CC
8	3, 5, 7	w3a 978	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		cmul 7791	. . . . 5 class x.
10	1, 4, 9	co 5865	. . . 4 class ( A x. B )
11	10, 6, 9	co 5865	. . 3 class ( ( A x. B ) x. C )
12	4, 6, 9	co 5865	. . . 4 class ( B x. C )
13	1, 12, 9	co 5865	. . 3 class ( A x. ( B x. C ) )
14	11, 13	wceq 1353	. 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  7917