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Theorem dffn5f 5904
 Description: Representation of a function in terms of its values. (Contributed by Mario Carneiro, 3-Jul-2015.)
Hypothesis
Ref Expression
dffn5f.1
Assertion
Ref Expression
dffn5f
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem dffn5f
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dffn5 5894 . 2
2 dffn5f.1 . . . . 5
3 nfcv 2564 . . . . 5
42, 3nffv 5856 . . . 4
5 nfcv 2564 . . . 4
6 fveq2 5849 . . . 4
74, 5, 6cbvmpt 4486 . . 3
87eqeq2i 2420 . 2
91, 8bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wb 184   wceq 1405  wnfc 2550   cmpt 4453   wfn 5564  cfv 5569 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4517  ax-nul 4525  ax-pr 4630 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-mo 2243  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-rab 2763  df-v 3061  df-sbc 3278  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4192  df-br 4396  df-opab 4454  df-mpt 4455  df-id 4738  df-xp 4829  df-rel 4830  df-cnv 4831  df-co 4832  df-dm 4833  df-iota 5533  df-fun 5571  df-fn 5572  df-fv 5577 This theorem is referenced by:  prdsgsum  17327  prdsgsumOLD  17328  lgamgulm2  23691  fcomptf  27942  esumsup  28536  refsum2cnlem1  36792  etransclem2  37387
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