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Theorem sbcthdv 2772
Description: Deduction version of sbcth 2771. (Contributed by NM, 30-Nov-2005.) (Proof shortened by Andrew Salmon, 8-Jun-2011.)
Hypothesis
Ref Expression
sbcthdv.1
Assertion
Ref Expression
sbcthdv  V  [.  ].
Distinct variable group:   ,
Allowed substitution hints:   ()   ()    V()

Proof of Theorem sbcthdv
StepHypRef Expression
1 sbcthdv.1 . . 3
21alrimiv 1751 . 2
3 spsbc 2769 . 2  V  [.  ].
42, 3mpan9 265 1  V  [.  ].
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wal 1240   wcel 1390   [.wsbc 2758
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-v 2553  df-sbc 2759
This theorem is referenced by: (None)
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