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Theorem dffun4 5549
Description: Alternate definition of a function. Definition 6.4(4) of [TakeutiZaring] p. 24. (Contributed by NM, 29-Dec-1996.)
Assertion
Ref Expression
dffun4
Distinct variable group:   , , ,

Proof of Theorem dffun4
StepHypRef Expression
1 dffun2 5547 . 2
2 df-br 4410 . . . . . . 7
3 df-br 4410 . . . . . . 7
42, 3anbi12i 697 . . . . . 6
54imbi1i 325 . . . . 5
65albii 1611 . . . 4
762albii 1612 . . 3
87anbi2i 694 . 2
91, 8bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1368  e.wcel 1758  <.cop 3999   class class class wbr 4409  Relwrel 4962  Funwfun 5531
This theorem is referenced by:  funopg  5569  funun  5579  fununi  5603  tfrlem7  6976  hashfun  12357  dffun10  28401  elfuns  28402  bnj1379  32667
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4530  ax-nul 4538  ax-pr 4648
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2805  df-rab 2809  df-v 3083  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3752  df-if 3906  df-sn 3994  df-pr 3996  df-op 4000  df-br 4410  df-opab 4468  df-id 4753  df-cnv 4965  df-co 4966  df-fun 5539
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