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Theorem rspsbc2VD 37245
Description: Virtual deduction proof of rspsbc2 36889. The following user's proof is completed by invoking mmj2's unify command and using mmj2's StepSelector to pick all remaining steps of the Metamath proof.
 1:: 2:: 3:: 4:1,3,?: e13 37129 5:1,4,?: e13 37129 6:2,5,?: e23 37136 7:6: 8:7: qed:8:
(Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
rspsbc2VD
Distinct variable groups:   ,   ,   ,,
Allowed substitution hints:   (,)   ()   ()   (,)

Proof of Theorem rspsbc2VD
StepHypRef Expression
1 idn2 36986 . . . . 5
2 idn1 36938 . . . . . 6
3 idn3 36988 . . . . . . 7
4 rspsbc 3345 . . . . . . 7
52, 3, 4e13 37129 . . . . . 6
6 sbcralg 3341 . . . . . . 7
76biimpd 211 . . . . . 6
82, 5, 7e13 37129 . . . . 5
9 rspsbc 3345 . . . . 5
101, 8, 9e23 37136 . . . 4
1110in3 36982 . . 3
1211in2 36978 . 2
1312in1 36935 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wcel 1886  wral 2736  wsbc 3266 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 986  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ral 2741  df-v 3046  df-sbc 3267  df-vd1 36934  df-vd2 36942  df-vd3 36954 This theorem is referenced by: (None)
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