ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fv0p1e1 Unicode version

Theorem fv0p1e1 8849
Description: Function value at  N  + 
1 with  N replaced by  0. Technical theorem to be used to reduce the size of a significant number of proofs. (Contributed by AV, 13-Aug-2022.)
Assertion
Ref Expression
fv0p1e1  |-  ( N  =  0  ->  ( F `  ( N  +  1 ) )  =  ( F ` 
1 ) )

Proof of Theorem fv0p1e1
StepHypRef Expression
1 oveq1 5781 . . 3  |-  ( N  =  0  ->  ( N  +  1 )  =  ( 0  +  1 ) )
2 0p1e1 8848 . . 3  |-  ( 0  +  1 )  =  1
31, 2syl6eq 2188 . 2  |-  ( N  =  0  ->  ( N  +  1 )  =  1 )
43fveq2d 5425 1  |-  ( N  =  0  ->  ( F `  ( N  +  1 ) )  =  ( F ` 
1 ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1331   ` cfv 5123  (class class class)co 5774   0cc0 7634   1c1 7635    + caddc 7637
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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-1cn 7727  ax-icn 7729  ax-addcl 7730  ax-mulcl 7732  ax-addcom 7734  ax-i2m1 7739  ax-0id 7742
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-v 2688  df-un 3075  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-iota 5088  df-fv 5131  df-ov 5777
This theorem is referenced by:  mertenslem2  11319
  Copyright terms: Public domain W3C validator