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Theorem funmpt2 5009
Description: Functionality of a class given by a "maps to" notation. (Contributed by FL, 17-Feb-2008.) (Revised by Mario Carneiro, 31-May-2014.)
Hypothesis
Ref Expression
funmpt2.1  |-  F  =  ( x  e.  A  |->  B )
Assertion
Ref Expression
funmpt2  |-  Fun  F

Proof of Theorem funmpt2
StepHypRef Expression
1 funmpt 5008 . 2  |-  Fun  (
x  e.  A  |->  B )
2 funmpt2.1 . . 3  |-  F  =  ( x  e.  A  |->  B )
32funeqi 4992 . 2  |-  ( Fun 
F  <->  Fun  ( x  e.  A  |->  B ) )
41, 3mpbir 144 1  |-  Fun  F
Colors of variables: wff set class
Syntax hints:    = wceq 1287    |-> cmpt 3868   Fun wfun 4966
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-14 1448  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-sep 3925  ax-pow 3977  ax-pr 4003
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-eu 1948  df-mo 1949  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360  df-rex 2361  df-v 2616  df-un 2990  df-in 2992  df-ss 2999  df-pw 3411  df-sn 3431  df-pr 3432  df-op 3434  df-br 3815  df-opab 3869  df-mpt 3870  df-id 4087  df-xp 4410  df-rel 4411  df-cnv 4412  df-co 4413  df-fun 4974
This theorem is referenced by:  fvmptss2  5327  frectfr  6100  frecsuclem  6106  djuun  6681  caseinj  6701  fihashf1rn  10046  exmidsbthrlem  11268
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