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Theorem bnj1465 28250
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1465.1
bnj1465.2
bnj1465.3
Assertion
Ref Expression
bnj1465
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem bnj1465
StepHypRef Expression
1 bnj1465.3 . . . . 5
21adantr 451 . . . 4
3 bnj1465.2 . . . . . 6
4 bnj1465.1 . . . . . 6
53, 4bnj1464 28249 . . . . 5
65adantl 452 . . . 4
72, 6mpbird 223 . . 3
8 sbc5 3015 . . 3
97, 8sylib 188 . 2
109bnj1266 28217 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1527  wex 1528   wceq 1623   wcel 1684  wsbc 2991 This theorem is referenced by:  bnj1463  28458 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-3an 936  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  df-sbc 2992
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