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Axiom ax-1rid 8740
Description:  1 is an identity element for real multiplication. Axiom 14 of 22 for real and complex numbers, justified by theorem ax1rid 8716. Weakened from the original axiom in the form of statement in mulid1 8767, 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 8669 . . 3  class  RR
31, 2wcel 1621 . 2  wff  A  e.  RR
4 c1 8671 . . . 4  class  1
5 cmul 8675 . . . 4  class  x.
61, 4, 5co 5757 . . 3  class  ( A  x.  1 )
76, 1wceq 1619 . 2  wff  ( A  x.  1 )  =  A
83, 7wi 6 1  wff  ( A  e.  RR  ->  ( A  x.  1 )  =  A )
Colors of variables: wff set class
This axiom is referenced by:  mulid1  8767  mulgt1  9548  ltmulgt11  9549  lemulge11  9551  addltmul  9879  xmulid1  10530  sqrlem7  11664  bezoutlem1  12644  nmopub2tALT  22414  nmfnleub2  22431
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