Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  elimhyp3v Structured version   Unicode version

Theorem elimhyp3v 3966
 Description: Eliminate a hypothesis containing 3 class variables. (Contributed by NM, 14-Aug-1999.)
Hypotheses
Ref Expression
elimhyp3v.1
elimhyp3v.2
elimhyp3v.3
elimhyp3v.4
elimhyp3v.5
elimhyp3v.6
elimhyp3v.7
Assertion
Ref Expression
elimhyp3v

Proof of Theorem elimhyp3v
StepHypRef Expression
1 iftrue 3912 . . . . . 6
21eqcomd 2428 . . . . 5
3 elimhyp3v.1 . . . . 5
42, 3syl 17 . . . 4
5 iftrue 3912 . . . . . 6
65eqcomd 2428 . . . . 5
7 elimhyp3v.2 . . . . 5
86, 7syl 17 . . . 4
9 iftrue 3912 . . . . . 6
109eqcomd 2428 . . . . 5
11 elimhyp3v.3 . . . . 5
1210, 11syl 17 . . . 4
134, 8, 123bitrd 282 . . 3
1413ibi 244 . 2
15 elimhyp3v.7 . . 3
16 iffalse 3915 . . . . . 6
1716eqcomd 2428 . . . . 5
18 elimhyp3v.4 . . . . 5
1917, 18syl 17 . . . 4
20 iffalse 3915 . . . . . 6
2120eqcomd 2428 . . . . 5
22 elimhyp3v.5 . . . . 5
2321, 22syl 17 . . . 4
24 iffalse 3915 . . . . . 6
2524eqcomd 2428 . . . . 5
26 elimhyp3v.6 . . . . 5
2725, 26syl 17 . . . 4
2819, 23, 273bitrd 282 . . 3
2915, 28mpbii 214 . 2
3014, 29pm2.61i 167 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wceq 1437  cif 3906 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-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-if 3907 This theorem is referenced by:  sseliALT  4549
 Copyright terms: Public domain W3C validator