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Axiom ax-1rid 8761
Description:  1 is an identity element for real multiplication. Axiom 14 of 22 for real and complex numbers, justified by theorem ax1rid 8737. Weakened from the original axiom in the form of statement in mulid1 8788, 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 8690 . . 3  class  RR
31, 2wcel 1621 . 2  wff  A  e.  RR
4 c1 8692 . . . 4  class  1
5 cmul 8696 . . . 4  class  x.
61, 4, 5co 5778 . . 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  8788  mulgt1  9569  ltmulgt11  9570  lemulge11  9572  addltmul  9900  xmulid1  10551  sqrlem7  11685  bezoutlem1  12665  nmopub2tALT  22435  nmfnleub2  22452
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