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Theorem sbcoreleleqVD 37250
Description: Virtual deduction proof of sbcoreleleq 36890. 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,?: e1a 37000 3:1,?: e1a 37000 4:1,?: e1a 37000 5:2,3,4,?: e111 37047 6:1,?: e1a 37000 7:5,6: e11 37061 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 36938 . . . . 5
2 sbcel2gv 3326 . . . . 5
31, 2e1a 37000 . . . 4
4 sbcel1gvOLD 37249 . . . . 5
51, 4e1a 37000 . . . 4
6 eqsbc3r 3323 . . . . 5
71, 6e1a 37000 . . . 4
8 3orbi123 36862 . . . . 5
983impexpbicomi 36829 . . . 4
103, 5, 7, 9e111 37047 . . 3
11 sbc3orgOLD 36887 . . . 4
121, 11e1a 37000 . . 3
13 biantr 941 . . . 4
1413expcom 437 . . 3
1510, 12, 14e11 37061 . 2
1615in1 36935 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   w3o 983   wceq 1443   wcel 1886  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-3or 985  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-v 3046  df-sbc 3267  df-vd1 36934 This theorem is referenced by: (None)
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