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Theorem sbcoreleleq 28619
 Description: Substitution of a set variable for another set variable in a 3-conjunct formula. Derived automatically from sbcoreleleqVD 28971. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
sbcoreleleq
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem sbcoreleleq
StepHypRef Expression
1 sbc3org 28616 . 2
2 sbcel2gv 3221 . . 3
3 sbcel1gv 3220 . . 3
4 eqsbc3r 3218 . . 3
5 3orbi123 28594 . . . 4
653impexpbicomi 1377 . . 3
72, 3, 4, 6syl3c 59 . 2
81, 7bitr4d 248 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   w3o 935   wceq 1652   wcel 1725  wsbc 3161 This theorem is referenced by:  tratrb  28620  tratrbVD  28973 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-3or 937  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-v 2958  df-sbc 3162
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