ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-addass Unicode version

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
StepHypRef Expression
1 cA . . . 4  class  A
2 cc 7292 . . . 4  class  CC
31, 2wcel 1436 . . 3  wff  A  e.  CC
4 cB . . . 4  class  B
54, 2wcel 1436 . . 3  wff  B  e.  CC
6 cC . . . 4  class  C
76, 2wcel 1436 . . 3  wff  C  e.  CC
83, 5, 7w3a 922 . 2  wff  ( A  e.  CC  /\  B  e.  CC  /\  C  e.  CC )
9 caddc 7297 . . . . 5  class  +
101, 4, 9co 5613 . . . 4  class  ( A  +  B )
1110, 6, 9co 5613 . . 3  class  ( ( A  +  B )  +  C )
124, 6, 9co 5613 . . . 4  class  ( B  +  C )
131, 12, 9co 5613 . . 3  class  ( A  +  ( B  +  C ) )
1411, 13wceq 1287 . 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  7416
  Copyright terms: Public domain W3C validator