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Theorem sbcoreleleq 36966
 Description: Substitution of a setvar variable for another setvar variable in a 3-conjunct formula. Derived automatically from sbcoreleleqVD 37319. (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 sbcel2gv 3315 . . 3
2 sbcel1v 3314 . . . 4
32a1i 11 . . 3
4 eqsbc3r 3312 . . 3
5 3orbi123 36938 . . . 4
653impexpbicomi 36905 . . 3
71, 3, 4, 6syl3c 62 . 2
8 sbc3or 36959 . 2
97, 8syl6rbbr 272 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   w3o 1006   wceq 1452   wcel 1904  wsbc 3255 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3or 1008  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-v 3033  df-sbc 3256 This theorem is referenced by:  tratrb  36967  tratrbVD  37321
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