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Theorem bnj92 29170
 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 3208 . 2
3 bnj92.2 . . 3
43bnj538 29045 . 2
5 sbcimg 3194 . . . . 5
63, 5ax-mp 8 . . . 4
7 sbcel2gv 3213 . . . . . 6
83, 7ax-mp 8 . . . . 5
93bnj525 29043 . . . . 5
108, 9imbi12i 317 . . . 4
116, 10bitri 241 . . 3
1211ralbii 2721 . 2
132, 4, 123bitri 263 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  wral 2697  cvv 2948  wsbc 3153  ciun 4085   csuc 4575  com 4837  cfv 5446   c-bnj14 28989 This theorem is referenced by:  bnj106  29176  bnj153  29188 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-ral 2702  df-v 2950  df-sbc 3154
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