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

Theorem sbcimdv 3395
 Description: Substitution analog of Theorem 19.20 of [Margaris] p. 90 (alim 1633). (Contributed by NM, 11-Nov-2005.) (Revised by NM, 17-Aug-2018.)
Hypothesis
Ref Expression
sbcimdv.1
Assertion
Ref Expression
sbcimdv
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem sbcimdv
StepHypRef Expression
1 sbcimdv.1 . . . 4
21alrimiv 1720 . . 3
3 spsbc 3340 . . 3
4 sbcim1 3376 . . 3
52, 3, 4syl56 34 . 2
6 sbcex 3337 . . . . 5
76con3i 135 . . . 4
87pm2.21d 106 . . 3
98a1d 25 . 2
105, 9pm2.61i 164 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4  wal 1393   wcel 1819  cvv 3109  wsbc 3327 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-12 1855  ax-13 2000  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328 This theorem is referenced by:  esum2dlem  28264
 Copyright terms: Public domain W3C validator