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Theorem bnj1388 29464
 Description: Technical lemma for bnj60 29493. 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
bnj1388.1
bnj1388.2
bnj1388.3
bnj1388.4
bnj1388.5
bnj1388.6
bnj1388.7
bnj1388.8
Assertion
Ref Expression
bnj1388
Distinct variable groups:   ,,   ,   ,   ,,   ,,   ,   ,   ,
Allowed substitution hints:   (,,)   (,,,)   (,,)   (,)   (,,)   (,,,)   (,,)   (,)   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1388
StepHypRef Expression
1 bnj1388.7 . . 3
2 nfv 1630 . . . 4
3 nfv 1630 . . . 4
4 nfra1 2758 . . . 4
52, 3, 4nf3an 1850 . . 3
61, 5nfxfr 1580 . 2
7 bnj1152 29429 . . . . . 6
87simplbi 448 . . . . 5
98adantl 454 . . . 4
107biimpi 188 . . . . . . . . 9
1110adantl 454 . . . . . . . 8
1211simprd 451 . . . . . . 7
131simp3bi 975 . . . . . . . 8
1413adantr 453 . . . . . . 7
15 df-ral 2712 . . . . . . . . 9
16 con2b 326 . . . . . . . . . 10
1716albii 1576 . . . . . . . . 9
1815, 17bitri 242 . . . . . . . 8
19 sp 1764 . . . . . . . . 9
2019impcom 421 . . . . . . . 8
2118, 20sylan2b 463 . . . . . . 7
2212, 14, 21syl2anc 644 . . . . . 6
23 bnj1388.5 . . . . . . . 8
2423eleq2i 2502 . . . . . . 7
25 nfcv 2574 . . . . . . . 8
26 nfcv 2574 . . . . . . . 8
27 bnj1388.8 . . . . . . . . . . 11
28 nfsbc1v 3182 . . . . . . . . . . 11
2927, 28nfxfr 1580 . . . . . . . . . 10
3029nfex 1866 . . . . . . . . 9
3130nfn 1812 . . . . . . . 8
32 sbceq1a 3173 . . . . . . . . . . 11
3332, 27syl6bbr 256 . . . . . . . . . 10
3433exbidv 1637 . . . . . . . . 9
3534notbid 287 . . . . . . . 8
3625, 26, 31, 35elrabf 3093 . . . . . . 7
3724, 36bitri 242 . . . . . 6
3822, 37sylnib 297 . . . . 5
39 iman 415 . . . . 5
4038, 39sylibr 205 . . . 4
419, 40mpd 15 . . 3
4241ex 425 . 2
436, 42ralrimi 2789 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360   w3a 937  wal 1550  wex 1551   wceq 1653   wcel 1726  cab 2424   wne 2601  wral 2707  wrex 2708  crab 2711  wsbc 3163   cun 3320   wss 3322  c0 3630  csn 3816  cop 3819   class class class wbr 4214   cdm 4880   cres 4882   wfn 5451  cfv 5456   c-bnj14 29114   w-bnj15 29118   c-bnj18 29120 This theorem is referenced by:  bnj1398  29465  bnj1489  29487 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-br 4215  df-bnj14 29115
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