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Theorem rspsbc2VD 28967
Description: Virtual deduction proof of rspsbc2 28618. 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 28860 5:1,4,?: e13 28860 6:2,5,?: e23 28867 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 28714 . . . . 5
2 idn1 28665 . . . . . 6
3 idn3 28716 . . . . . . 7
4 rspsbc 3239 . . . . . . 7
52, 3, 4e13 28860 . . . . . 6
6 sbcralg 3235 . . . . . . 7
76biimpd 199 . . . . . 6
82, 5, 7e13 28860 . . . . 5
9 rspsbc 3239 . . . . 5
101, 8, 9e23 28867 . . . 4
1110in3 28710 . . 3
1211in2 28706 . 2
1312in1 28662 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1725  wral 2705  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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-v 2958  df-sbc 3162  df-vd1 28661  df-vd2 28670  df-vd3 28682
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