Axiom ax-addass 7210

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axaddass 7170. Proofs should normally use addass 7235 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 7111	. . . 4 class CC
3	1, 2	wcel 1434	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1434	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1434	. . 3 wff C e. CC
8	3, 5, 7	w3a 920	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 7116	. . . . 5 class +
10	1, 4, 9	co 5564	. . . 4 class ( A + B )
11	10, 6, 9	co 5564	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5564	. . . 4 class ( B + C )
13	1, 12, 9	co 5564	. . 3 class ( A + ( B + C ) )
14	11, 13	wceq 1285	. 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  7235