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

Theorem ssres 5175
 Description: Subclass theorem for restriction. (Contributed by NM, 16-Aug-1994.)
Assertion
Ref Expression
ssres

Proof of Theorem ssres
StepHypRef Expression
1 ssrin 3568 . 2
2 df-res 4893 . 2
3 df-res 4893 . 2
41, 2, 33sstr4g 3391 1
 Colors of variables: wff set class Syntax hints:   wi 4  cvv 2958   cin 3321   wss 3322   cxp 4879   cres 4883 This theorem is referenced by:  imass1  5242  marypha1lem  7441  sspg  22232  ssps  22234  sspn  22240 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-in 3329  df-ss 3336  df-res 4893
 Copyright terms: Public domain W3C validator