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Theorem residm 5584
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 3761 . 2 𝐵𝐵
2 resabs2 5583 . 2 (𝐵𝐵 → ((𝐴𝐵) ↾ 𝐵) = (𝐴𝐵))
31, 2ax-mp 5 1 ((𝐴𝐵) ↾ 𝐵) = (𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1628  wss 3711  cres 5264
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1867  ax-4 1882  ax-5 1984  ax-6 2050  ax-7 2086  ax-9 2144  ax-10 2164  ax-11 2179  ax-12 2192  ax-13 2387  ax-ext 2736  ax-sep 4929  ax-nul 4937  ax-pr 5051
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1631  df-ex 1850  df-nf 1855  df-sb 2043  df-clab 2743  df-cleq 2749  df-clel 2752  df-nfc 2887  df-rab 3055  df-v 3338  df-dif 3714  df-un 3716  df-in 3718  df-ss 3725  df-nul 4055  df-if 4227  df-sn 4318  df-pr 4320  df-op 4324  df-opab 4861  df-xp 5268  df-rel 5269  df-res 5274
This theorem is referenced by:  resima  5585  dffv2  6429  fvsnun2  6609  qtopres  21699  bnj1253  31388  eldioph2lem1  37821  eldioph2lem2  37822  relexpiidm  38494
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