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Theorem sbcoreleleqVD 29033
Description: Virtual deduction proof of sbcoreleleq 28681. 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:: 2:1,?: e1_ 28790 3:1,?: e1_ 28790 4:1,?: e1_ 28790 5:2,3,4,?: e111 28837 6:1,?: e1_ 28790 7:5,6: e11 28851 qed:7:
(Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sbcoreleleqVD
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem sbcoreleleqVD
StepHypRef Expression
1 idn1 28727 . . . . 5
2 sbcel2gv 3223 . . . . 5
31, 2e1_ 28790 . . . 4
4 sbcel1gv 3222 . . . . 5
51, 4e1_ 28790 . . . 4
6 eqsbc3r 3220 . . . . 5
71, 6e1_ 28790 . . . 4
8 3orbi123 28656 . . . . 5
983impexpbicomi 1378 . . . 4
103, 5, 7, 9e111 28837 . . 3
11 sbc3org 28678 . . . 4
121, 11e1_ 28790 . . 3
13 biantr 899 . . . 4
1413expcom 426 . . 3
1510, 12, 14e11 28851 . 2
1615in1 28724 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   w3o 936   wceq 1653   wcel 1726  wsbc 3163 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-sbc 3164  df-vd1 28723
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