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Theorem bnj1148 29590
 Description: Property of . (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj1148

Proof of Theorem bnj1148
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elisset 3089 . . . . 5
21adantl 467 . . . 4
3 bnj93 29459 . . . . 5
4 eleq1 2492 . . . . . . 7
54anbi2d 708 . . . . . 6
6 bnj602 29511 . . . . . . 7
76eleq1d 2489 . . . . . 6
85, 7imbi12d 321 . . . . 5
93, 8mpbii 214 . . . 4
102, 9bnj593 29340 . . 3
1110bnj937 29368 . 2
1211pm2.43i 49 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wceq 1437  wex 1659   wcel 1867  cvv 3078   c-bnj14 29278   w-bnj15 29282 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ral 2778  df-rab 2782  df-v 3080  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-sn 3994  df-pr 3996  df-op 4000  df-br 4418  df-bnj14 29279  df-bnj13 29281  df-bnj15 29283 This theorem is referenced by:  bnj1136  29591  bnj1413  29629
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