Axiom ax-addass 8026

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axaddass 7984. Proofs should normally use addass 8054 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 7922	. . . 4 class CC
3	1, 2	wcel 2175	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2175	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2175	. . 3 wff C e. CC
8	3, 5, 7	w3a 980	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 7927	. . . . 5 class +
10	1, 4, 9	co 5943	. . . 4 class ( A + B )
11	10, 6, 9	co 5943	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5943	. . . 4 class ( B + C )
13	1, 12, 9	co 5943	. . 3 class ( A + ( B + C ) )
14	11, 13	wceq 1372	. 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  8054