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Theorem pm13.183 3068
 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 2441 . 2
2 eqeq2 2444 . . . 4
32bibi1d 311 . . 3
43albidv 1635 . 2
5 eqeq2 2444 . . . 4
65alrimiv 1641 . . 3
7 stdpc4 2087 . . . 4
8 sbbi 2145 . . . . 5
9 eqsb3 2536 . . . . . . 7
109bibi2i 305 . . . . . 6
11 equsb1 2113 . . . . . . 7
12 bi1 179 . . . . . . 7
1311, 12mpi 17 . . . . . 6
1410, 13sylbi 188 . . . . 5
158, 14sylbi 188 . . . 4
167, 15syl 16 . . 3
176, 16impbii 181 . 2
181, 4, 17vtoclbg 3004 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549   wceq 1652  wsb 1658   wcel 1725 This theorem is referenced by:  mpt22eqb  6171 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
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