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Theorem sbcimdv 3209
 Description: Substitution analog of Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 11-Nov-2005.)
Hypothesis
Ref Expression
sbcimdv.1
Assertion
Ref Expression
sbcimdv
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem sbcimdv
StepHypRef Expression
1 sbcimdv.1 . . . . 5
21alrimiv 1641 . . . 4
3 spsbc 3160 . . . 4
42, 3syl5 30 . . 3
5 sbcimg 3189 . . 3
64, 5sylibd 206 . 2
76impcom 420 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1549   wcel 1725  wsbc 3148 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 2411 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2417  df-cleq 2423  df-clel 2426  df-nfc 2555  df-v 2945  df-sbc 3149
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