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Theorem pm13.183 2845
 Description: Compare theorem *13.183 in [WhiteheadRussell] p. 178. Only is required to be a set. (Contributed by Andrew Salmon, 3-Jun-2011.)
Assertion
Ref Expression
pm13.183
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem pm13.183
StepHypRef Expression
1 eqeq1 2259 . 2
2 eqeq2 2262 . . . 4
32bibi1d 312 . . 3
43albidv 2004 . 2
5 eqeq2 2262 . . . 4
65alrimiv 2012 . . 3
7 stdpc4 1896 . . . 4
8 sbbi 1963 . . . . 5
9 eqsb3 2350 . . . . . . 7
109bibi2i 306 . . . . . 6
11 equsb1 1906 . . . . . . 7
12 bi1 180 . . . . . . 7
1311, 12mpi 18 . . . . . 6
1410, 13sylbi 189 . . . . 5
158, 14sylbi 189 . . . 4
167, 15syl 17 . . 3
176, 16impbii 182 . 2
181, 4, 17vtoclbg 2782 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178  wal 1532   wceq 1619   wcel 1621  wsb 1882 This theorem is referenced by:  mpt22eqb  5805 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 1926  ax-ext 2234 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 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729
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