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Theorem dffun4 5466
 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 5464 . 2
2 df-br 4213 . . . . . . 7
3 df-br 4213 . . . . . . 7
42, 3anbi12i 679 . . . . . 6
54imbi1i 316 . . . . 5
65albii 1575 . . . 4
762albii 1576 . . 3
87anbi2i 676 . 2
91, 8bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wcel 1725  cop 3817   class class class wbr 4212   wrel 4883   wfun 5448 This theorem is referenced by:  funopg  5485  funun  5495  fununi  5517  tfrlem7  6644  hashfun  11700  dffun10  25759  elfuns  25760  bnj1379  29202 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-id 4498  df-cnv 4886  df-co 4887  df-fun 5456
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