Axiom ax-addass 8281

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axaddass 8239. Proofs should normally use addass 8309 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 8177	. . . 4 class CC
3	1, 2	wcel 2209	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2209	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2209	. . 3 wff C e. CC
8	3, 5, 7	w3a 1009	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 8182	. . . . 5 class +
10	1, 4, 9	co 6085	. . . 4 class ( A + B )
11	10, 6, 9	co 6085	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 6085	. . . 4 class ( B + C )
13	1, 12, 9	co 6085	. . 3 class ( A + ( B + C ) )
14	11, 13	wceq 1402	. 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 used by:  addass  8309