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Theorem sbcthdv 3176
 Description: Deduction version of sbcth 3175. (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:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem sbcthdv
StepHypRef Expression
1 sbcthdv.1 . . 3
21alrimiv 1641 . 2
3 spsbc 3173 . 2
42, 3mpan9 456 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wal 1549   wcel 1725  wsbc 3161 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-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-v 2958  df-sbc 3162
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