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Theorem bnj1172 29370
 Description: Technical lemma for bnj69 29379. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1172.3
bnj1172.96
bnj1172.113
Assertion
Ref Expression
bnj1172

Proof of Theorem bnj1172
StepHypRef Expression
1 bnj1172.96 . . 3
2 bnj1172.113 . . . . . . . 8
32imbi1d 309 . . . . . . 7
43pm5.32i 619 . . . . . 6
54imbi2i 304 . . . . 5
65albii 1575 . . . 4
76exbii 1592 . . 3
81, 7mpbi 200 . 2
9 simp3 959 . . . . . . 7
10 bnj1172.3 . . . . . . 7
119, 10syl6eleq 2526 . . . . . 6
12 elin 3530 . . . . . . 7
1312simprbi 451 . . . . . 6
1411, 13syl 16 . . . . 5
1514anim1i 552 . . . 4
1615imim2i 14 . . 3
1716alimi 1568 . 2
188, 17bnj101 29088 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   w3a 936  wal 1549  wex 1550   wceq 1652   wcel 1725   cin 3319   class class class wbr 4212   c-bnj18 29058 This theorem is referenced by:  bnj1190  29377 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-in 3327
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