Axiom ax-addass 7078

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axaddass 7038. Proofs should normally use addass 7103 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 6979	. . . 4 class CC
3	1, 2	wcel 1433	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1433	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1433	. . 3 wff C e. CC
8	3, 5, 7	w3a 919	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 6984	. . . . 5 class +
10	1, 4, 9	co 5532	. . . 4 class ( A + B )
11	10, 6, 9	co 5532	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5532	. . . 4 class ( B + C )
13	1, 12, 9	co 5532	. . 3 class ( A + ( B + C ) )
14	11, 13	wceq 1284	. 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  7103