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Theorem pm13.183 2979
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 2359 . 2
2 eqeq2 2362 . . . 4
32bibi1d 310 . . 3
43albidv 1625 . 2
5 eqeq2 2362 . . . 4
65alrimiv 1631 . . 3
7 stdpc4 2024 . . . 4
8 sbbi 2071 . . . . 5
9 eqsb3 2454 . . . . . . 7
109bibi2i 304 . . . . . 6
11 equsb1 2034 . . . . . . 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 2915 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176  wal 1540   wceq 1642  wsb 1648   wcel 1710
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861
This theorem is referenced by: (None)
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