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Axiom ax-1rid 8804
Description:  1 is an identity element for real multiplication. Axiom 14 of 22 for real and complex numbers, justified by theorem ax1rid 8780. Weakened from the original axiom in the form of statement in mulid1 8832, 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 8733 . . 3  class  RR
31, 2wcel 1687 . 2  wff  A  e.  RR
4 c1 8735 . . . 4  class  1
5 cmul 8739 . . . 4  class  x.
61, 4, 5co 5821 . . 3  class  ( A  x.  1 )
76, 1wceq 1625 . 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  8832  mulgt1  9612  ltmulgt11  9613  lemulge11  9615  addltmul  9944  xmulid1  10595  sqrlem7  11730  bezoutlem1  12713  nmopub2tALT  22483  nmfnleub2  22500
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