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Theorem sbeqalb 3352
 Description: Theorem *14.121 in [WhiteheadRussell] p. 185. (Contributed by Andrew Salmon, 28-Jun-2011.) (Proof shortened by Wolf Lammen, 9-May-2013.)
Assertion
Ref Expression
sbeqalb
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbeqalb
StepHypRef Expression
1 bibi1 328 . . . . 5
21biimpa 486 . . . 4
32biimpd 210 . . 3
43alanimi 1682 . 2
5 sbceqal 3351 . 2
64, 5syl5 33 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wal 1435   wceq 1437   wcel 1872 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-v 3082  df-sbc 3300 This theorem is referenced by:  iotaval  5576
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