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Theorem dffn5imf 5476
 Description: Representation of a function in terms of its values. (Contributed by Jim Kingdon, 31-Dec-2018.)
Hypothesis
Ref Expression
dffn5imf.1
Assertion
Ref Expression
dffn5imf
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem dffn5imf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dffn5im 5467 . 2
2 dffn5imf.1 . . . 4
3 nfcv 2281 . . . 4
42, 3nffv 5431 . . 3
5 nfcv 2281 . . 3
6 fveq2 5421 . . 3
74, 5, 6cbvmpt 4023 . 2
81, 7syl6eq 2188 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1331  wnfc 2268   cmpt 3989   wfn 5118  cfv 5123 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-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-sbc 2910  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-opab 3990  df-mpt 3991  df-id 4215  df-xp 4545  df-rel 4546  df-cnv 4547  df-co 4548  df-dm 4549  df-iota 5088  df-fun 5125  df-fn 5126  df-fv 5131 This theorem is referenced by: (None)
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