Axiom ax-addass 7851

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axaddass 7809. Proofs should normally use addass 7879 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 7747	. . . 4 class CC
3	1, 2	wcel 2136	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2136	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2136	. . 3 wff C e. CC
8	3, 5, 7	w3a 968	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 7752	. . . . 5 class +
10	1, 4, 9	co 5841	. . . 4 class ( A + B )
11	10, 6, 9	co 5841	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5841	. . . 4 class ( B + C )
13	1, 12, 9	co 5841	. . 3 class ( A + ( B + C ) )
14	11, 13	wceq 1343	. 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  7879