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Theorem bnj1476 29610
 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 3720 . . . . 5
3 bnj1476.1 . . . . . . . . 9
4 nfrab1 2948 . . . . . . . . 9
53, 4nfcxfr 2567 . . . . . . . 8
65nfcri 2563 . . . . . . 7
76nfn 1960 . . . . . 6
8 nfv 1755 . . . . . 6
9 eleq1 2494 . . . . . . 7
109notbid 295 . . . . . 6
117, 8, 10cbval 2086 . . . . 5
122, 11bitri 252 . . . 4
131, 12sylib 199 . . 3
143rabeq2i 3019 . . . . . . 7
1514notbii 297 . . . . . 6
1615biimpi 197 . . . . 5
17 iman 425 . . . . 5
1816, 17sylibr 215 . . . 4
1918alimi 1678 . . 3
2013, 19syl 17 . 2
2120bnj1142 29553 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370  wal 1435   wceq 1437   wcel 1872  wral 2714  crab 2718  c0 3704 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ne 2601  df-ral 2719  df-rab 2723  df-v 3024  df-dif 3382  df-nul 3705 This theorem is referenced by:  bnj1312  29819
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