Axiom ax-addass 7746

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axaddass 7704. Proofs should normally use addass 7774 instead. (New usage is discouraged.) (Contributed by NM, 22-Nov-1994.)

Assertion

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

Detailed syntax breakdown of Axiom ax-addass

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		cC	. . . 4 class C
7	6, 2	wcel 1481	. . 3 wff C e. CC
8	3, 5, 7	w3a 963	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 7647	. . . . 5 class +
10	1, 4, 9	co 5782	. . . 4 class ( A + B )
11	10, 6, 9	co 5782	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5782	. . . 4 class ( B + C )
13	1, 12, 9	co 5782	. . 3 class ( A + ( B + C ) )
14	11, 13	wceq 1332	. 2 wff ( ( A + B ) + C ) = ( A + ( B + C ) )
15	8, 14	wi 4	1 wff ( ( A e. CC /\ B e. CC /\ C e. CC ) -> ( ( A + B ) + C ) = ( A + ( B + C ) ) )

This axiom is referenced by:  addass  7774