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Theorem lhpexle1lem 33325
 Description: Lemma for lhpexle1 33326 and others that eliminates restrictions on . (Contributed by NM, 24-Jul-2013.)
Hypotheses
Ref Expression
lhpexle1lem.1
lhpexle1lem.2
Assertion
Ref Expression
lhpexle1lem
Distinct variable groups:   ,   ,   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem lhpexle1lem
StepHypRef Expression
1 lhpexle1lem.1 . . . 4
21adantr 466 . . 3
3 simprl 762 . . . . . 6
4 simprr 764 . . . . . 6
5 simplr 760 . . . . . . 7
6 simpllr 767 . . . . . . 7
7 nelne2 2752 . . . . . . 7
85, 6, 7syl2anc 665 . . . . . 6
93, 4, 83jca 1185 . . . . 5
109ex 435 . . . 4
1110reximdva 2898 . . 3
122, 11mpd 15 . 2
131adantr 466 . . 3
14 simprl 762 . . . . . 6
15 simprr 764 . . . . . 6
16 simplr 760 . . . . . . 7
17 nbrne2 4435 . . . . . . 7
1814, 16, 17syl2anc 665 . . . . . 6
1914, 15, 183jca 1185 . . . . 5
2019ex 435 . . . 4
2120reximdv 2897 . . 3
2213, 21mpd 15 . 2
23 lhpexle1lem.2 . 2
2412, 22, 23pm2.61dda 800 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370   w3a 982   wcel 1867   wne 2616  wrex 2774   class class class wbr 4417 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-ral 2778  df-rex 2779  df-rab 2782  df-v 3080  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-sn 3994  df-pr 3996  df-op 4000  df-br 4418 This theorem is referenced by:  lhpexle1  33326  lhpexle2  33328  lhpexle3  33330
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