Axiom ax-addass 7974

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axaddass 7932. Proofs should normally use addass 8002 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 7870	. . . 4 class CC
3	1, 2	wcel 2164	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2164	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2164	. . 3 wff C e. CC
8	3, 5, 7	w3a 980	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 7875	. . . . 5 class +
10	1, 4, 9	co 5918	. . . 4 class ( A + B )
11	10, 6, 9	co 5918	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5918	. . . 4 class ( B + C )
13	1, 12, 9	co 5918	. . 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  8002