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Theorem sbeqalb 3177
 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 1568 . 2
5 sbceqal 3176 . 2
64, 5syl5 30 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1546   wceq 1649   wcel 1721 This theorem is referenced by:  iotaval  5392 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-v 2922  df-sbc 3126
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