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Theorem sbeqalb 3018
 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 319 . . . . 5
21biimpa 472 . . . 4
32biimpd 200 . . 3
43alanimi 1550 . 2
5 sbceqal 3017 . 2
64, 5syl5 30 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532   wceq 1619   wcel 1621 This theorem is referenced by:  iotaval  6236 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2239 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-v 2765  df-sbc 2967
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