ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  1e0p1 Unicode version

Theorem 1e0p1 9230
Description: The successor of zero. (Contributed by Mario Carneiro, 18-Feb-2014.)
Assertion
Ref Expression
1e0p1  |-  1  =  ( 0  +  1 )

Proof of Theorem 1e0p1
StepHypRef Expression
1 0p1e1 8841 . 2  |-  ( 0  +  1 )  =  1
21eqcomi 2143 1  |-  1  =  ( 0  +  1 )
Colors of variables: wff set class
Syntax hints:    = wceq 1331  (class class class)co 5774   0cc0 7627   1c1 7628    + caddc 7630
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2121  ax-1cn 7720  ax-icn 7722  ax-addcl 7723  ax-mulcl 7725  ax-addcom 7727  ax-i2m1 7732  ax-0id 7735
This theorem depends on definitions:  df-bi 116  df-cleq 2132  df-clel 2135
This theorem is referenced by:  6p5e11  9261  7p4e11  9264  8p3e11  9269  9p2e11  9275  fz1ssfz0  9904  fzo01  10000  bcp1nk  10515  arisum2  11275  ege2le3  11384  ef4p  11407  efgt1p2  11408  efgt1p  11409  ennnfonelem1  11927  dveflem  12865
  Copyright terms: Public domain W3C validator