Axiom ax-mulcom 7721

Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7679. Proofs should normally use mulcom 7749 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 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	3, 5	wa 103	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7625	. . . 4 class x.
8	1, 4, 7	co 5774	. . 3 class ( A x. B )
9	4, 1, 7	co 5774	. . 3 class ( B x. A )
10	8, 9	wceq 1331	. 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  7749