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Theorem dffun9 5621
Description: Alternate definition of a function. (Contributed by NM, 28-Mar-2007.) (Revised by NM, 16-Jun-2017.)
Assertion
Ref Expression
dffun9
Distinct variable group:   , ,

Proof of Theorem dffun9
StepHypRef Expression
1 dffun7 5619 . 2
2 vex 3112 . . . . . . . 8
3 vex 3112 . . . . . . . 8
42, 3brelrn 5238 . . . . . . 7
54pm4.71ri 633 . . . . . 6
65mobii 2307 . . . . 5
7 df-rmo 2815 . . . . 5
86, 7bitr4i 252 . . . 4
98ralbii 2888 . . 3
109anbi2i 694 . 2
111, 10bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  e.wcel 1818  E*wmo 2283  A.wral 2807  E*wrmo 2810   class class class wbr 4452  domcdm 5004  rancrn 5005  Relwrel 5009  Funwfun 5587
This theorem is referenced by:  brdom4  8929
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rmo 2815  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-id 4800  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-fun 5595
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