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Theorem elrnmptdv 4802
 Description: Elementhood in the range of a function in maps-to notation, deduction form. (Contributed by Rohan Ridenour, 3-Aug-2023.)
Hypotheses
Ref Expression
elrnmptdv.1
elrnmptdv.2
elrnmptdv.3
elrnmptdv.4
Assertion
Ref Expression
elrnmptdv
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem elrnmptdv
StepHypRef Expression
1 elrnmptdv.4 . . 3
2 elrnmptdv.2 . . 3
31, 2rspcime 2801 . 2
4 elrnmptdv.3 . . 3
5 elrnmptdv.1 . . . 4
65elrnmpt 4797 . . 3
74, 6syl 14 . 2
83, 7mpbird 166 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1332   wcel 1481  wrex 2418   cmpt 3998   crn 4549 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-sep 4055  ax-pow 4107  ax-pr 4140 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-eu 2003  df-mo 2004  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-v 2692  df-un 3081  df-in 3083  df-ss 3090  df-pw 3518  df-sn 3539  df-pr 3540  df-op 3542  df-br 3939  df-opab 3999  df-mpt 4000  df-cnv 4556  df-dm 4558  df-rn 4559 This theorem is referenced by: (None)
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