Axiom ax-mulcom 7596

Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by theorem axmulcom 7556. Proofs should normally use mulcom 7621 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 7498	. . . 4 class CC
3	1, 2	wcel 1448	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1448	. . 3 wff B e. CC
6	3, 5	wa 103	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7505	. . . 4 class x.
8	1, 4, 7	co 5706	. . 3 class ( A x. B )
9	4, 1, 7	co 5706	. . 3 class ( B x. A )
10	8, 9	wceq 1299	. 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  7621