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Theorem bnj1476 28549
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1476.1
bnj1476.2
Assertion
Ref Expression
bnj1476

Proof of Theorem bnj1476
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj1476.2 . . . 4
2 eq0 3578 . . . . 5
3 bnj1476.1 . . . . . . . . 9
4 nfrab1 2824 . . . . . . . . 9
53, 4nfcxfr 2513 . . . . . . . 8
65nfcri 2510 . . . . . . 7
76nfn 1801 . . . . . 6
8 nfv 1626 . . . . . 6
9 eleq1 2440 . . . . . . 7
109notbid 286 . . . . . 6
117, 8, 10cbval 2010 . . . . 5
122, 11bitri 241 . . . 4
131, 12sylib 189 . . 3
143rabeq2i 2889 . . . . . . 7
1514notbii 288 . . . . . 6
1615biimpi 187 . . . . 5
17 iman 414 . . . . 5
1816, 17sylibr 204 . . . 4
1918alimi 1565 . . 3
2013, 19syl 16 . 2
2120bnj1142 28491 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1546   wceq 1649   wcel 1717  wral 2642  crab 2646  c0 3564 This theorem is referenced by:  bnj1312  28758 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-ne 2545  df-ral 2647  df-rab 2651  df-v 2894  df-dif 3259  df-nul 3565
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