Axiom ax-mulcom 7887

Description: Multiplication of complex numbers is commutative. Axiom for real and complex numbers, justified by Theorem axmulcom 7845. Proofs should normally use mulcom 7915 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 7784	. . . 4 class CC
3	1, 2	wcel 2146	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2146	. . 3 wff B e. CC
6	3, 5	wa 104	. 2 wff ( A e. CC /\ B e. CC )
7		cmul 7791	. . . 4 class x.
8	1, 4, 7	co 5865	. . 3 class ( A x. B )
9	4, 1, 7	co 5865	. . 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  7915