Axiom ax-addass 7043

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axaddass 7003. Proofs should normally use addass 7068 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 6944	. . . 4 class CC
3	1, 2	wcel 1409	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1409	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1409	. . 3 wff C e. CC
8	3, 5, 7	w3a 896	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 6949	. . . . 5 class +
10	1, 4, 9	co 5539	. . . 4 class ( A + B )
11	10, 6, 9	co 5539	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5539	. . . 4 class ( B + C )
13	1, 12, 9	co 5539	. . 3 class ( A + ( B + C ) )
14	11, 13	wceq 1259	. 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  7068