Axiom ax-mulcom 7348

Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7308. Proofs should normally use mulcom 7373 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 7250	. . . 4 class CC
3	1, 2	wcel 1434	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1434	. . 3 wff B e. CC
6	3, 5	wa 102	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7257	. . . 4 class x.
8	1, 4, 7	co 5590	. . 3 class ( A x. B )
9	4, 1, 7	co 5590	. . 3 class ( B x. A )
10	8, 9	wceq 1285	. 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  7373