Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  resmpo Unicode version

Theorem resmpo 5916
 Description: Restriction of the mapping operation. (Contributed by Mario Carneiro, 17-Dec-2013.)
Assertion
Ref Expression
resmpo
Distinct variable groups:   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem resmpo
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 resoprab2 5915 . 2
2 df-mpo 5826 . . 3
32reseq1i 4861 . 2
4 df-mpo 5826 . 2
51, 3, 43eqtr4g 2215 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1335   wcel 2128   wss 3102   cxp 4583   cres 4587  coprab 5822   cmpo 5823 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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-14 2131  ax-ext 2139  ax-sep 4082  ax-pow 4135  ax-pr 4169 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rex 2441  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-pw 3545  df-sn 3566  df-pr 3567  df-op 3569  df-opab 4026  df-xp 4591  df-rel 4592  df-res 4597  df-oprab 5825  df-mpo 5826 This theorem is referenced by:  ofmres  6081  divfnzn  9523  txss12  12637  txbasval  12638  cnmpt2res  12668
 Copyright terms: Public domain W3C validator