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Theorem fv0p1e1 9010
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 5875 . . 3  |-  ( N  =  0  ->  ( N  +  1 )  =  ( 0  +  1 ) )
2 0p1e1 9009 . . 3  |-  ( 0  +  1 )  =  1
31, 2eqtrdi 2226 . 2  |-  ( N  =  0  ->  ( N  +  1 )  =  1 )
43fveq2d 5514 1  |-  ( N  =  0  ->  ( F `  ( N  +  1 ) )  =  ( F ` 
1 ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1353   ` cfv 5211  (class class class)co 5868   0cc0 7789   1c1 7790    + caddc 7792
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-1cn 7882  ax-icn 7884  ax-addcl 7885  ax-mulcl 7887  ax-addcom 7889  ax-i2m1 7894  ax-0id 7897
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2739  df-un 3133  df-sn 3597  df-pr 3598  df-op 3600  df-uni 3808  df-br 4001  df-iota 5173  df-fv 5219  df-ov 5871
This theorem is referenced by:  mertenslem2  11515  fprodfac  11594
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