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Theorem pm13.183 2733
 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
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq1 2088 . 2
2 eqeq2 2091 . . . 4
32bibi1d 231 . . 3
43albidv 1746 . 2
5 eqeq2 2091 . . . 4
65alrimiv 1796 . . 3
7 stdpc4 1699 . . . 4
8 sbbi 1875 . . . . 5
9 eqsb3 2183 . . . . . . 7
109bibi2i 225 . . . . . 6
11 equsb1 1709 . . . . . . 7
12 bi1 116 . . . . . . 7
1311, 12mpi 15 . . . . . 6
1410, 13sylbi 119 . . . . 5
158, 14sylbi 119 . . . 4
167, 15syl 14 . . 3
176, 16impbii 124 . 2
181, 4, 17vtoclbg 2660 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103  wal 1283   wceq 1285   wcel 1434  wsb 1686 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604 This theorem is referenced by:  mpt22eqb  5641
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