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Axiom ax-addass 7210
Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axaddass 7170. Proofs should normally use addass 7235 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 7111 . . . 4  class  CC
31, 2wcel 1434 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1434 . . 3  wff  B  e.  CC
6 cC . . . 4  class  C
76, 2wcel 1434 . . 3  wff  C  e.  CC
83, 5, 7w3a 920 . 2  wff  ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )
9 caddc 7116 . . . . 5  class  +
101, 4, 9co 5564 . . . 4  class  ( A  +  B )
1110, 6, 9co 5564 . . 3  class  ( ( A  +  B )  +  C )
124, 6, 9co 5564 . . . 4  class  ( B  +  C )
131, 12, 9co 5564 . . 3  class  ( A  +  ( B  +  C ) )
1411, 13wceq 1285 . 2  wff  ( ( A  +  B )  +  C )  =  ( A  +  ( B  +  C ) )
158, 14wi 4 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  7235
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