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Theorem tz6.12-2 5112
Description: Function value when  F is not a function. Theorem 6.12(2) of [TakeutiZaring] p. 27. (Contributed by NM, 30-Apr-2004.) (Proof shortened by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
tz6.12-2  F  F `  (/)
Distinct variable groups:   , F   ,

Proof of Theorem tz6.12-2
StepHypRef Expression
1 df-fv 4853 . 2  F `
 iota F
2 iotanul 4825 . 2  F  iota F  (/)
31, 2syl5eq 2081 1  F  F `  (/)
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wceq 1242  weu 1897   (/)c0 3218   class class class wbr 3755   iotacio 4808   ` cfv 4845
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643  df-eu 1900  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-dif 2914  df-in 2918  df-ss 2925  df-nul 3219  df-sn 3373  df-uni 3572  df-iota 4810  df-fv 4853
This theorem is referenced by:  fvprc  5115  ndmfvg  5147  nfunsn  5150
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