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Theorem elrnmpt2d 4834
 Description: Elementhood in the range of a function in maps-to notation, deduction form. (Contributed by Rohan Ridenour, 3-Aug-2023.)
Hypotheses
Ref Expression
elrnmpt2d.1
elrnmpt2d.2
Assertion
Ref Expression
elrnmpt2d
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem elrnmpt2d
StepHypRef Expression
1 elrnmpt2d.2 . 2
2 elrnmpt2d.1 . . . 4
32elrnmpt 4828 . . 3
43ibi 175 . 2
51, 4syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1332   wcel 2125  wrex 2433   cmpt 4021   crn 4580 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 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-14 2128  ax-ext 2136  ax-sep 4078  ax-pow 4130  ax-pr 4164 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-eu 2006  df-mo 2007  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-rex 2438  df-v 2711  df-un 3102  df-in 3104  df-ss 3111  df-pw 3541  df-sn 3562  df-pr 3563  df-op 3565  df-br 3962  df-opab 4022  df-mpt 4023  df-cnv 4587  df-dm 4589  df-rn 4590 This theorem is referenced by: (None)
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