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Theorem sbeqalb 3205
 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 318 . . . . 5
21biimpa 471 . . . 4
32biimpd 199 . . 3
43alanimi 1571 . 2
5 sbceqal 3204 . 2
64, 5syl5 30 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wceq 1652   wcel 1725 This theorem is referenced by:  iotaval  5421 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 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sbc 3154
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