Axiom ax-addass 7722

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axaddass 7680. Proofs should normally use addass 7750 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 7618	. . . 4 class CC
3	1, 2	wcel 1480	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1480	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1480	. . 3 wff C e. CC
8	3, 5, 7	w3a 962	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 7623	. . . . 5 class +
10	1, 4, 9	co 5774	. . . 4 class ( A + B )
11	10, 6, 9	co 5774	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5774	. . . 4 class ( B + C )
13	1, 12, 9	co 5774	. . 3 class ( A + ( B + C ) )
14	11, 13	wceq 1331	. 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  7750