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

Step	Hyp	Ref	Expression
1		uneq1 3650	. . 3
2		undif1 3903	. . 3
3		uncom 3647	. . . 4
4		enp1ilem.1	. . . 4
5	3, 4	eqtr4i 2489	. . 3
6	1, 2, 5	3eqtr3g 2521	. 2
7		snssi 4174	. . . 4
8		ssequn2 3676	. . . 4
9	7, 8	sylib 196	. . 3
10	9	eqeq1d 2459	. 2
11	6, 10	syl5ib 219	1

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