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Theorem bnj521 29041
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj521

Proof of Theorem bnj521
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elirr 7558 . . . 4
2 elin 3522 . . . . . 6
3 elsn 3821 . . . . . . 7
4 eleq1 2495 . . . . . . . 8
54biimpac 473 . . . . . . 7
63, 5sylan2b 462 . . . . . 6
72, 6sylbi 188 . . . . 5
87exlimiv 1644 . . . 4
91, 8mto 169 . . 3
10 n0 3629 . . 3
119, 10mtbir 291 . 2
12 nne 2602 . 2
1311, 12mpbi 200 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 359  wex 1550   wceq 1652   wcel 1725   wne 2598   cin 3311  c0 3620  csn 3806 This theorem is referenced by:  bnj927  29076  bnj535  29198 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395  ax-reg 7552 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-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-nul 3621  df-sn 3812  df-pr 3813
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