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Theorem sbcthdv 3343
Description: Deduction version of sbcth 3342. (Contributed by NM, 30-Nov-2005.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypothesis
Ref Expression
sbcthdv.1
Assertion
Ref Expression
sbcthdv
Distinct variable group:   ,

Proof of Theorem sbcthdv
StepHypRef Expression
1 sbcthdv.1 . . 3
21alrimiv 1719 . 2
3 spsbc 3340 . 2
42, 3mpan9 469 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  e.wcel 1818  [.wsbc 3327
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328
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