Axiom ax-mulcom 7390

Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7350. Proofs should normally use mulcom 7415 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 7292	. . . 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	3, 5	wa 102	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7299	. . . 4 class x.
8	1, 4, 7	co 5613	. . 3 class ( A x. B )
9	4, 1, 7	co 5613	. . 3 class ( B x. A )
10	8, 9	wceq 1287	. 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  7415