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Theorem dffun8 5297
 Description: Alternate definition of a function. One possibility for the definition of a function in [Enderton] p. 42. Compare dffun7 5296. (Contributed by NM, 4-Nov-2002.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Assertion
Ref Expression
dffun8
Distinct variable group:   ,,

Proof of Theorem dffun8
StepHypRef Expression
1 dffun7 5296 . 2
2 df-mo 2161 . . . . 5
3 vex 2804 . . . . . . 7
43eldm 4892 . . . . . 6
5 pm5.5 326 . . . . . 6
64, 5sylbi 187 . . . . 5
72, 6syl5bb 248 . . . 4
87ralbiia 2588 . . 3
98anbi2i 675 . 2
101, 9bitri 240 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wex 1531   wcel 1696  weu 2156  wmo 2157  wral 2556   class class class wbr 4039   cdm 4705   wrel 4710   wfun 5265 This theorem is referenced by:  dfdfat2  28099 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-opab 4094  df-id 4325  df-cnv 4713  df-co 4714  df-dm 4715  df-fun 5273
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