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

Theorem sbciedf 3196
 Description: Conversion of implicit substitution to explicit class substitution, deduction form. (Contributed by NM, 29-Dec-2014.)
Hypotheses
Ref Expression
sbcied.1
sbcied.2
sbciedf.3
sbciedf.4
Assertion
Ref Expression
sbciedf
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem sbciedf
StepHypRef Expression
1 sbcied.1 . 2
2 sbciedf.4 . 2
3 sbciedf.3 . . 3
4 sbcied.2 . . . 4
54ex 424 . . 3
63, 5alrimi 1781 . 2
7 sbciegft 3191 . 2
81, 2, 6, 7syl3anc 1184 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wnf 1553   wceq 1652   wcel 1725  wsbc 3161 This theorem is referenced by:  sbcied  3197  sbc2iegf  3227  csbiebt  3287  sbcnestgf  3298  ovmpt2dxf  6199 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 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-v 2958  df-sbc 3162
 Copyright terms: Public domain W3C validator