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Axiom ax-addass 7734
Description: Addition of complex numbers is associative. Axiom for real and complex numbers, justified by theorem axaddass 7692. Proofs should normally use addass 7762 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 7630 . . . 4  class  CC
31, 2wcel 1480 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1480 . . 3  wff  B  e.  CC
6 cC . . . 4  class  C
76, 2wcel 1480 . . 3  wff  C  e.  CC
83, 5, 7w3a 962 . 2  wff  ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )
9 caddc 7635 . . . . 5  class  +
101, 4, 9co 5774 . . . 4  class  ( A  +  B )
1110, 6, 9co 5774 . . 3  class  ( ( A  +  B )  +  C )
124, 6, 9co 5774 . . . 4  class  ( B  +  C )
131, 12, 9co 5774 . . 3  class  ( A  +  ( B  +  C ) )
1411, 13wceq 1331 . 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  7762
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