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Theorem enp1ilem 7774
 Description: Lemma for uses of enp1i 7775. (Contributed by Mario Carneiro, 5-Jan-2016.)
Hypothesis
Ref Expression
enp1ilem.1
Assertion
Ref Expression
enp1ilem

Proof of Theorem enp1ilem
StepHypRef Expression
1 uneq1 3650 . . 3
2 undif1 3903 . . 3
3 uncom 3647 . . . 4
4 enp1ilem.1 . . . 4
53, 4eqtr4i 2489 . . 3
61, 2, 53eqtr3g 2521 . 2
7 snssi 4174 . . . 4
8 ssequn2 3676 . . . 4
97, 8sylib 196 . . 3
109eqeq1d 2459 . 2
116, 10syl5ib 219 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  e.wcel 1818  \cdif 3472  u.cun 3473  C_wss 3475  {csn 4029 This theorem is referenced by:  en2  7776  en3  7777  en4  7778 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-sn 4030
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