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Theorem resmpt2 6160
 Description: Restriction of the mapping operation. (Contributed by Mario Carneiro, 17-Dec-2013.)
Assertion
Ref Expression
resmpt2
Distinct variable groups:   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem resmpt2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 resoprab2 6159 . 2
2 df-mpt2 6078 . . 3
32reseq1i 5134 . 2
4 df-mpt2 6078 . 2
51, 3, 43eqtr4g 2492 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725   wss 3312   cxp 4868   cres 4872  coprab 6074   cmpt2 6075 This theorem is referenced by:  ofmres  6335  cantnfval2  7616  sylow3lem5  15257  txss12  17629  txbasval  17630  cnmpt2res  17701  fmucndlem  18313  cnmpt2pc  18945  oprpiece1res1  18968  oprpiece1res2  18969  cxpcn3  20624  ressplusf  24175  cvmlift2lem6  24987  cvmlift2lem12  24993 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-opab 4259  df-xp 4876  df-rel 4877  df-res 4882  df-oprab 6077  df-mpt2 6078
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