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Theorem mptfng 5573
 Description: The maps-to notation defines a function with domain. (Contributed by Scott Fenton, 21-Mar-2011.)
Hypothesis
Ref Expression
mptfng.1
Assertion
Ref Expression
mptfng
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem mptfng
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eueq 3108 . . 3
21ralbii 2731 . 2
3 mptfng.1 . . . 4
4 df-mpt 4271 . . . 4
53, 4eqtri 2458 . . 3
65fnopabg 5571 . 2
72, 6bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wceq 1653   wcel 1726  weu 2283  wral 2707  cvv 2958  copab 4268   cmpt 4269   wfn 5452 This theorem is referenced by:  fnmpt  5574  fnmpti  5576  mpteqb  5822  bdayfo  25635  fobigcup  25750  ofmpteq  26789  dihf11lem  32137 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-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-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-fun 5459  df-fn 5460
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