Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  sbcied2 Structured version   Unicode version

Theorem sbcied2 3200
 Description: Conversion of implicit substitution to explicit class substitution, deduction form. (Contributed by NM, 13-Dec-2014.)
Hypotheses
Ref Expression
sbcied2.1
sbcied2.2
sbcied2.3
Assertion
Ref Expression
sbcied2
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem sbcied2
StepHypRef Expression
1 sbcied2.1 . 2
2 id 21 . . . 4
3 sbcied2.2 . . . 4
42, 3sylan9eqr 2492 . . 3
5 sbcied2.3 . . 3
64, 5syldan 458 . 2
71, 6sbcied 3199 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360   wceq 1653   wcel 1726  wsbc 3163 This theorem is referenced by:  iscat  13899  sectffval  13978  issubc  14037  isfunc  14063  ismnd  14694  isnsg  14971  isrng  15670  islbs  16150  isdomn  16356  isassa  16377  opsrval  16537 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-3an 939  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-sbc 3164
 Copyright terms: Public domain W3C validator