Axiom ax-mulcom 7845

Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by Theorem axmulcom 7803. Proofs should normally use mulcom 7873 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 7742	. . . 4 class CC
3	1, 2	wcel 2135	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2135	. . 3 wff B e. CC
6	3, 5	wa 103	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7749	. . . 4 class x.
8	1, 4, 7	co 5836	. . 3 class ( A x. B )
9	4, 1, 7	co 5836	. . 3 class ( B x. A )
10	8, 9	wceq 1342	. 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  7873