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Axiom ax-addass 8798
Description: Addition of complex numbers is associative. Axiom 9 of 22 for real and complex numbers, justified by theorem axaddass 8774. Proofs should normally use addass 8820 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
StepHypRef Expression
1 cA . . . 4  class  A
2 cc 8731 . . . 4  class  CC
31, 2wcel 1685 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1685 . . 3  wff  B  e.  CC
6 cC . . . 4  class  C
76, 2wcel 1685 . . 3  wff  C  e.  CC
83, 5, 7w3a 936 . 2  wff  ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )
9 caddc 8736 . . . . 5  class  +
101, 4, 9co 5820 . . . 4  class  ( A  +  B )
1110, 6, 9co 5820 . . 3  class  ( ( A  +  B )  +  C )
124, 6, 9co 5820 . . . 4  class  ( B  +  C )
131, 12, 9co 5820 . . 3  class  ( A  +  ( B  +  C ) )
1411, 13wceq 1624 . 2  wff  ( ( A  +  B )  +  C )  =  ( A  +  ( B  +  C ) )
158, 14wi 6 1  wff  ( ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )  ->  (
( A  +  B
)  +  C )  =  ( A  +  ( B  +  C
) ) )
Colors of variables: wff set class
This axiom is referenced by:  addass  8820
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