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Theorem chfnrn 5844
 Description: The range of a choice function (a function that chooses an element from each member of its domain) is included in the union of its domain. (Contributed by NM, 31-Aug-1999.)
Assertion
Ref Expression
chfnrn
Distinct variable groups:   ,   ,

Proof of Theorem chfnrn
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fvelrnb 5777 . . . . 5
21biimpd 200 . . . 4
3 eleq1 2498 . . . . . . 7
43biimpcd 217 . . . . . 6
54ralimi 2783 . . . . 5
6 rexim 2812 . . . . 5
75, 6syl 16 . . . 4
82, 7sylan9 640 . . 3
9 eluni2 4021 . . 3
108, 9syl6ibr 220 . 2
1110ssrdv 3356 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726  wral 2707  wrex 2708   wss 3322  cuni 4017   crn 4882   wfn 5452  cfv 5457 This theorem is referenced by:  stoweidlem59  27798 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4333  ax-nul 4341  ax-pr 4406 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-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  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 4216  df-opab 4270  df-mpt 4271  df-id 4501  df-xp 4887  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-iota 5421  df-fun 5459  df-fn 5460  df-fv 5465
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