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Theorem mptresid 4688
 Description: The restricted identity expressed with the "maps to" notation. (Contributed by FL, 25-Apr-2012.)
Assertion
Ref Expression
mptresid
Distinct variable group:   ,

Proof of Theorem mptresid
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-mpt 3848 . 2
2 opabresid 4687 . 2
31, 2eqtri 2076 1
 Colors of variables: wff set class Syntax hints:   wa 101   wceq 1259   wcel 1409  copab 3845   cmpt 3846   cid 4053   cres 4375 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-14 1421  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-sep 3903  ax-pow 3955  ax-pr 3972 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-v 2576  df-un 2950  df-in 2952  df-ss 2959  df-pw 3389  df-sn 3409  df-pr 3410  df-op 3412  df-opab 3847  df-mpt 3848  df-id 4058  df-xp 4379  df-rel 4380  df-res 4385 This theorem is referenced by:  idref  5424
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