Axiom ax-addass 7942

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axaddass 7900. Proofs should normally use addass 7970 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 7838	. . . 4 class CC
3	1, 2	wcel 2160	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2160	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2160	. . 3 wff C e. CC
8	3, 5, 7	w3a 980	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 7843	. . . . 5 class +
10	1, 4, 9	co 5895	. . . 4 class ( A + B )
11	10, 6, 9	co 5895	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5895	. . . 4 class ( B + C )
13	1, 12, 9	co 5895	. . 3 class ( A + ( B + C ) )
14	11, 13	wceq 1364	. 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  7970