Axiom ax-mulcom 8273

Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by Theorem axmulcom 8231. Proofs should normally use mulcom 8301 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 8170	. . . 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 8177	. . . 4 class x.
8	1, 4, 7	co 6078	. . 3 class ( A x. B )
9	4, 1, 7	co 6078	. . 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 referenced by:  mulcom  8301