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Theorem residm 5571
Description: Idempotent law for restriction. (Contributed by NM, 27-Mar-1998.)
Assertion
Ref Expression
residm ((𝐴𝐵) ↾ 𝐵) = (𝐴𝐵)

Proof of Theorem residm
StepHypRef Expression
1 ssid 3773 . 2 𝐵𝐵
2 resabs2 5570 . 2 (𝐵𝐵 → ((𝐴𝐵) ↾ 𝐵) = (𝐴𝐵))
31, 2ax-mp 5 1 ((𝐴𝐵) ↾ 𝐵) = (𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1631  wss 3723  cres 5251
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4915  ax-nul 4923  ax-pr 5034
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-3an 1073  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-rab 3070  df-v 3353  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-nul 4064  df-if 4226  df-sn 4317  df-pr 4319  df-op 4323  df-opab 4847  df-xp 5255  df-rel 5256  df-res 5261
This theorem is referenced by:  resima  5572  dffv2  6413  fvsnun2  6593  qtopres  21722  bnj1253  31423  eldioph2lem1  37849  eldioph2lem2  37850  relexpiidm  38522
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