MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax-1rid Unicode version

Axiom ax-1rid 8687
Description:  1 is an identity element for real multiplication. Axiom 14 of 22 for real and complex numbers, justified by theorem ax1rid 8663. Weakened from the original axiom in the form of statement in mulid1 8714, 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 8616 . . 3  class  RR
31, 2wcel 1621 . 2  wff  A  e.  RR
4 c1 8618 . . . 4  class  1
5 cmul 8622 . . . 4  class  x.
61, 4, 5co 5710 . . 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  8714  mulgt1  9495  ltmulgt11  9496  lemulge11  9498  addltmul  9826  xmulid1  10477  sqrlem7  11611  bezoutlem1  12591  nmopub2tALT  22319  nmfnleub2  22336
  Copyright terms: Public domain W3C validator