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Axiom ax-1rid 8807
Description:  1 is an identity element for real multiplication. Axiom 14 of 22 for real and complex numbers, justified by theorem ax1rid 8783. Weakened from the original axiom in the form of statement in mulid1 8835, based on ideas by Eric Schmidt. (Contributed by NM, 29-Jan-1995.)
Assertion
Ref Expression
ax-1rid  |-  ( A  e.  RR  ->  ( A  x.  1 )  =  A )

Detailed syntax breakdown of Axiom ax-1rid
StepHypRef Expression
1 cA . . 3  class  A
2 cr 8736 . . 3  class  RR
31, 2wcel 1684 . 2  wff  A  e.  RR
4 c1 8738 . . . 4  class  1
5 cmul 8742 . . . 4  class  x.
61, 4, 5co 5858 . . 3  class  ( A  x.  1 )
76, 1wceq 1623 . 2  wff  ( A  x.  1 )  =  A
83, 7wi 4 1  wff  ( A  e.  RR  ->  ( A  x.  1 )  =  A )
Colors of variables: wff set class
This axiom is referenced by:  mulid1  8835  mulgt1  9615  ltmulgt11  9616  lemulge11  9618  addltmul  9947  xmulid1  10599  sqrlem7  11734  bezoutlem1  12717  nmopub2tALT  22489  nmfnleub2  22506  unitdivcld  23285
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