Axiom ax-addass 8057

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by Theorem axaddass 8015. Proofs should normally use addass 8085 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 7953	. . . 4 class CC
3	1, 2	wcel 2177	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 2177	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 2177	. . 3 wff C e. CC
8	3, 5, 7	w3a 981	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 7958	. . . . 5 class +
10	1, 4, 9	co 5962	. . . 4 class ( A + B )
11	10, 6, 9	co 5962	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5962	. . . 4 class ( B + C )
13	1, 12, 9	co 5962	. . 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  8085