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Theorem bnj92 29461
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj92.1
bnj92.2
Assertion
Ref Expression
bnj92
Distinct variable groups:   ,   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,)   (,,)   (,,)

Proof of Theorem bnj92
StepHypRef Expression
1 bnj92.1 . . 3
21sbcbii 3361 . 2
3 bnj92.2 . . 3
43bnj538 29337 . 2
5 sbcimg 3347 . . . . 5
63, 5ax-mp 5 . . . 4
7 sbcel2gv 3365 . . . . . 6
83, 7ax-mp 5 . . . . 5
93bnj525 29335 . . . . 5
108, 9imbi12i 327 . . . 4
116, 10bitri 252 . . 3
1211ralbii 2863 . 2
132, 4, 123bitri 274 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wceq 1437   wcel 1870  wral 2782  cvv 3087  wsbc 3305  ciun 4302   csuc 5444  cfv 5601  com 6706   c-bnj14 29281 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 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 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 1790  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ral 2787  df-v 3089  df-sbc 3306 This theorem is referenced by:  bnj106  29467  bnj153  29479
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