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Theorem bnj563 32754
 Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj563.19
bnj563.21
Assertion
Ref Expression
bnj563

Proof of Theorem bnj563
StepHypRef Expression
1 bnj563.19 . . 3
2 bnj312 32719 . . . . 5
3 bnj252 32710 . . . . 5
42, 3bitri 249 . . . 4
54simplbi 460 . . 3
61, 5sylbi 195 . 2
7 bnj563.21 . . . 4
87simp2bi 1007 . . 3
97simp3bi 1008 . . 3
108, 9jca 532 . 2
11 necom 2729 . . . 4
12 eleq2 2533 . . . . . . 7
1312biimpa 484 . . . . . 6
14 elsuci 4937 . . . . . . . 8
15 orcom 387 . . . . . . . . 9
16 neor 2784 . . . . . . . . 9
1715, 16bitr3i 251 . . . . . . . 8
1814, 17sylib 196 . . . . . . 7
1918imp 429 . . . . . 6
2013, 19sylan 471 . . . . 5
21203impa 1186 . . . 4
2211, 21syl3an3b 1261 . . 3
23223expb 1192 . 2
246, 10, 23syl2an 477 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wo 368   wa 369   w3a 968   wceq 1374   wcel 1762   wne 2655   csuc 4873  com 6671   w-bnj17 32693 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1961  ax-ext 2438 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 970  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2446  df-cleq 2452  df-clel 2455  df-nfc 2610  df-ne 2657  df-v 3108  df-un 3474  df-sn 4021  df-suc 4877  df-bnj17 32694 This theorem is referenced by:  bnj570  32917
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