Axiom ax-mulcom 8046

Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by Theorem axmulcom 8004. Proofs should normally use mulcom 8074 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 7943	. . . 4 class CC
3	1, 2	wcel 2177	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2177	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7950	. . . 4 class x.
8	1, 4, 7	co 5957	. . 3 class ( A x. B )
9	4, 1, 7	co 5957	. . 3 class ( B x. A )
10	8, 9	wceq 1373	. 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  8074