Axiom ax-mulcom 7912

Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by Theorem axmulcom 7870. Proofs should normally use mulcom 7940 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 7809	. . . 4 class CC
3	1, 2	wcel 2148	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2148	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7816	. . . 4 class x.
8	1, 4, 7	co 5875	. . 3 class ( A x. B )
9	4, 1, 7	co 5875	. . 3 class ( B x. A )
10	8, 9	wceq 1353	. 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  7940