Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  residm Structured version   Unicode version

Theorem residm 5177
 Description: Idempotent law for restriction. (Contributed by NM, 27-Mar-1998.)
Assertion
Ref Expression
residm

Proof of Theorem residm
StepHypRef Expression
1 ssid 3367 . 2
2 resabs2 5176 . 2
31, 2ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wceq 1652   wss 3320   cres 4880 This theorem is referenced by:  resima  5178  dffv2  5796  fvsnun2  5929  qtopres  17730  eldioph2lem1  26818  eldioph2lem2  26819  bnj1253  29386 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 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-opab 4267  df-xp 4884  df-rel 4885  df-res 4890
 Copyright terms: Public domain W3C validator