Axiom ax-addcom 7744

Description: Addition commutes. Axiom for real and complex numbers, justified by theorem axaddcom 7702. Proofs should normally use addcom 7923 instead. (New usage is discouraged.) (Contributed by Jim Kingdon, 17-Jan-2020.)

Assertion

Ref	Expression
ax-addcom	|- ( ( A e. CC /\ B e. CC ) -> ( A + B ) = ( B + A ) )

Detailed syntax breakdown of Axiom ax-addcom

Step	Hyp	Ref	Expression
1		cA	. . . 4 class A
2		cc 7642	. . . 4 class CC
3	1, 2	wcel 1481	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1481	. . 3 wff B e. CC
6	3, 5	wa 103	. 2 wff ( A e. CC /\ B e. CC )
7		caddc 7647	. . . 4 class +
8	1, 4, 7	co 5782	. . 3 class ( A + B )
9	4, 1, 7	co 5782	. . 3 class ( B + A )
10	8, 9	wceq 1332	. 2 wff ( A + B ) = ( B + A )
11	6, 10	wi 4	1 wff ( ( A e. CC /\ B e. CC ) -> ( A + B ) = ( B + A ) )

This axiom is referenced by:  addcom  7923