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Theorem pm13.183 2908
 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 2289 . 2
2 eqeq2 2292 . . . 4
32bibi1d 310 . . 3
43albidv 1611 . 2
5 eqeq2 2292 . . . 4
65alrimiv 1617 . . 3
7 stdpc4 1964 . . . 4
8 sbbi 2011 . . . . 5
9 eqsb3 2384 . . . . . . 7
109bibi2i 304 . . . . . 6
11 equsb1 1974 . . . . . . 7
12 bi1 178 . . . . . . 7
1311, 12mpi 16 . . . . . 6
1410, 13sylbi 187 . . . . 5
158, 14sylbi 187 . . . 4
167, 15syl 15 . . 3
176, 16impbii 180 . 2
181, 4, 17vtoclbg 2844 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1527   wceq 1623  wsb 1629   wcel 1684 This theorem is referenced by:  mpt22eqb  5953 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790
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