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Theorem eupath2lem2 21692
 Description: Lemma for eupath2 21694. (Contributed by Mario Carneiro, 8-Apr-2015.)
Hypothesis
Ref Expression
eupath2lem2.1
Assertion
Ref Expression
eupath2lem2

Proof of Theorem eupath2lem2
StepHypRef Expression
1 eqidd 2436 . . . . . . 7
21olcd 383 . . . . . 6
32biantrud 494 . . . . 5
4 eupath2lem2.1 . . . . . 6
5 eupath2lem1 21691 . . . . . 6
64, 5ax-mp 8 . . . . 5
73, 6syl6bbr 255 . . . 4
8 simpr 448 . . . . 5
98eleq1d 2501 . . . 4
107, 9bitrd 245 . . 3
1110necon1bbid 2652 . 2
12 simpl 444 . . . . . . 7
13 neeq1 2606 . . . . . . 7
1412, 13syl5ibcom 212 . . . . . 6
1514pm4.71rd 617 . . . . 5
16 eqcom 2437 . . . . 5
17 ancom 438 . . . . 5
1815, 16, 173bitr4g 280 . . . 4
1912neneqd 2614 . . . . . . 7
20 biorf 395 . . . . . . 7
2119, 20syl 16 . . . . . 6
22 orcom 377 . . . . . 6
2321, 22syl6bb 253 . . . . 5
2423anbi1d 686 . . . 4
2518, 24bitrd 245 . . 3
26 ancom 438 . . 3
2725, 26syl6bbr 255 . 2
28 eupath2lem1 21691 . . . 4
294, 28ax-mp 8 . . 3
308eleq1d 2501 . . 3
3129, 30syl5bbr 251 . 2
3211, 27, 313bitrd 271 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359   wceq 1652   wcel 1725   wne 2598  cvv 2948  c0 3620  cif 3731  cpr 3807 This theorem is referenced by:  eupath2lem3  21693 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 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-v 2950  df-dif 3315  df-un 3317  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813
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