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Theorem dmfex 5628
 Description: If a mapping is a set, its domain is a set. (Contributed by NM, 27-Aug-2006.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Assertion
Ref Expression
dmfex

Proof of Theorem dmfex
StepHypRef Expression
1 fdm 5597 . . 3
2 dmexg 5132 . . . 4
3 eleq1 2498 . . . 4
42, 3syl5ib 212 . . 3
51, 4syl 16 . 2
65impcom 421 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  cvv 2958   cdm 4880  wf 5452 This theorem is referenced by:  wemoiso  6080  fopwdom  7218  fowdom  7541  wdomfil  7944  fin23lem17  8220  fin23lem32  8226  fin23lem39  8232  enfin1ai  8266  fin1a2lem7  8288  kelac1  27140  lindfmm  27276 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405  ax-un 4703 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-cnv 4888  df-dm 4890  df-rn 4891  df-fn 5459  df-f 5460
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