Axiom ax-addass 7391

Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axaddass 7351. Proofs should normally use addass 7416 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 7292	. . . 4 class CC
3	1, 2	wcel 1436	. . 3 wff A e. CC
4		cB	. . . 4 class B
5	4, 2	wcel 1436	. . 3 wff B e. CC
6		cC	. . . 4 class C
7	6, 2	wcel 1436	. . 3 wff C e. CC
8	3, 5, 7	w3a 922	. 2 wff ( A e. CC /\ B e. CC /\ C e. CC )
9		caddc 7297	. . . . 5 class +
10	1, 4, 9	co 5613	. . . 4 class ( A + B )
11	10, 6, 9	co 5613	. . 3 class ( ( A + B ) + C )
12	4, 6, 9	co 5613	. . . 4 class ( B + C )
13	1, 12, 9	co 5613	. . 3 class ( A + ( B + C ) )
14	11, 13	wceq 1287	. 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  7416