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Theorem resmpt2 6400
Description: Restriction of the mapping operation. (Contributed by Mario Carneiro, 17-Dec-2013.)
Assertion
Ref Expression
resmpt2
Distinct variable groups:   , ,   , ,   , ,   , ,

Proof of Theorem resmpt2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 resoprab2 6399 . 2
2 df-mpt2 6301 . . 3
32reseq1i 5274 . 2
4 df-mpt2 6301 . 2
51, 3, 43eqtr4g 2523 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  C_wss 3475  X.cxp 5002  |`cres 5006  {coprab 6297  e.cmpt2 6298
This theorem is referenced by:  ofmres  6796  cantnfval2  8109  cantnfval2OLD  8139  pgrpsubgsymg  16433  sylow3lem5  16651  mamures  18892  mdetrsca2  19106  mdetrlin2  19109  mdetunilem5  19118  smadiadetglem1  19173  smadiadetglem2  19174  pmatcollpw3lem  19284  txss12  20106  txbasval  20107  cnmpt2res  20178  fmucndlem  20794  cnmpt2pc  21428  oprpiece1res1  21451  oprpiece1res2  21452  cxpcn3  23122  ressplusf  27638  cvmlift2lem6  28753  cvmlift2lem12  28759  rngchomrnghmresOLD  32804  rhmsubclem1  32894  rhmsubcOLDlem1  32913
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-xp 5010  df-rel 5011  df-res 5016  df-oprab 6300  df-mpt2 6301
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