Axiom ax-mulcom 8280

Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by Theorem axmulcom 8238. Proofs should normally use mulcom 8308 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 8177	. . . 4 class CC
3	1, 2	wcel 2209	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2209	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 8184	. . . 4 class x.
8	1, 4, 7	co 6085	. . 3 class ( A x. B )
9	4, 1, 7	co 6085	. . 3 class ( B x. A )
10	8, 9	wceq 1402	. 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 used by:  mulcom  8308