Home

Metamath Proof Explorer

< Previous   Next > Related theorems Unicode version

---

Theorem sbthlem3 4429

Description: Lemma for sbth 4437.

Hypotheses

Ref	Expression
sbthlem.1
sbthlem.2

Assertion

Ref	Expression
sbthlem3

Distinct variable groups:   ,   ,   ,   ,   ,

---

Proof of Theorem sbthlem3

Step	Hyp	Ref	Expression
1		sbthlem.1	. . . . . 6
2		sbthlem.2	. . . . . 6
3	1, 2	sbthlem2 4428	. . . . 5
4	1, 2	sbthlem1 4427	. . . . 5
5	3, 4	jctil 292	. . . 4
6		eqss 2067	. . . 4
7	5, 6	sylibr 200	. . 3
8	7	difeq2d 2149	. 2
9		imassrn 3399	. . . 4
10		sstr2 2061	. . . 4
11	9, 10	ax-mp 7	. . 3
12		dfss4 2232	. . 3
13	11, 12	sylib 198	. 2
14	8, 13	eqtr2d 1500	1

Colors of variables: wff set class

Syntax hints:   wi 3   wa 223   wceq 953   wcel 955  cab 1456  cvv 1802   cdif 2034   wss 2037  cuni 2493   crn 3161  cima 3163

This theorem is referenced by:  sbthlem4 4430  sbthlem5 4431

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-13 966  ax-14 967  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452  ax-sep 2693  ax-pow 2732  ax-pr 2769

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376  df-clab 1457  df-cleq 1462  df-clel 1465  df-ne 1579  df-ral 1641  df-rex 1642  df-v 1803  df-dif 2039  df-un 2040  df-in 2041  df-ss 2043  df-nul 2271  df-pw 2392  df-sn 2402  df-pr 2403  df-op 2406  df-uni 2494  df-br 2610  df-opab 2657  df-xp 3174  df-rel 3175  df-cnv 3176  df-dm 3178  df-rn 3179  df-res 3180  df-ima 3181

Copyright terms: Public domain