Axiom ax-mulcom 8025

Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by Theorem axmulcom 7983. Proofs should normally use mulcom 8053 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 7922	. . . 4 class CC
3	1, 2	wcel 2175	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2175	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7929	. . . 4 class x.
8	1, 4, 7	co 5943	. . 3 class ( A x. B )
9	4, 1, 7	co 5943	. . 3 class ( B x. A )
10	8, 9	wceq 1372	. 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  8053