Axiom ax-addass 8027

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axaddass 7985. Proofs should normally use addass 8055 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 7923	. . . 4 class CC
3	1, 2	wcel 2176	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2176	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2176	. . 3 wff C e. CC
8	3, 5, 7	w3a 981	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 7928	. . . . 5 class +
10	1, 4, 9	co 5944	. . . 4 class ( A + B )
11	10, 6, 9	co 5944	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5944	. . . 4 class ( B + C )
13	1, 12, 9	co 5944	. . 3 class ( A + ( B + C ) )
14	11, 13	wceq 1373	. 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  8055