Axiom ax-mulcom 10000

Description: Multiplication of complex numbers is commutative. Axiom 8 of 22 for real and complex numbers, justified by theorem axmulcom 9976. Proofs should normally use mulcom 10022 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)

Assertion

Ref	Expression
ax-mulcom	|- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )

Detailed syntax breakdown of Axiom ax-mulcom

Step	Hyp	Ref	Expression
1		cA	. . . 4 class A
2		cc 9934	. . . 4 class CC
3	1, 2	wcel 1990	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1990	. . 3 wff B e. CC
6	3, 5	wa 384	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 9941	. . . 4 class x.
8	1, 4, 7	co 6650	. . 3 class ( A x. B )
9	4, 1, 7	co 6650	. . 3 class ( B x. A )
10	8, 9	wceq 1483	. 2 wff ( A x. B ) = ( B x. A )
11	6, 10	wi 4	1 wff ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )

This axiom is referenced by:  mulcom  10022