MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  keephyp3v Unicode version

Theorem keephyp3v 4008
Description: Keep a hypothesis containing 3 class variables. (Contributed by NM, 27-Sep-1999.)
Hypotheses
Ref Expression
keephyp3v.1
keephyp3v.2
keephyp3v.3
keephyp3v.4
keephyp3v.5
keephyp3v.6
keephyp3v.7
keephyp3v.8
Assertion
Ref Expression
keephyp3v

Proof of Theorem keephyp3v
StepHypRef Expression
1 keephyp3v.7 . . 3
2 iftrue 3947 . . . . . 6
32eqcomd 2465 . . . . 5
4 keephyp3v.1 . . . . 5
53, 4syl 16 . . . 4
6 iftrue 3947 . . . . . 6
76eqcomd 2465 . . . . 5
8 keephyp3v.2 . . . . 5
97, 8syl 16 . . . 4
10 iftrue 3947 . . . . . 6
1110eqcomd 2465 . . . . 5
12 keephyp3v.3 . . . . 5
1311, 12syl 16 . . . 4
145, 9, 133bitrd 279 . . 3
151, 14mpbii 211 . 2
16 keephyp3v.8 . . 3
17 iffalse 3950 . . . . . 6
1817eqcomd 2465 . . . . 5
19 keephyp3v.4 . . . . 5
2018, 19syl 16 . . . 4
21 iffalse 3950 . . . . . 6
2221eqcomd 2465 . . . . 5
23 keephyp3v.5 . . . . 5
2422, 23syl 16 . . . 4
25 iffalse 3950 . . . . . 6
2625eqcomd 2465 . . . . 5
27 keephyp3v.6 . . . . 5
2826, 27syl 16 . . . 4
2920, 24, 283bitrd 279 . . 3
3016, 29mpbii 211 . 2
3115, 30pm2.61i 164 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  =wceq 1395  ifcif 3941
This theorem is referenced by:  sseliALT  4583
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-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-if 3942
  Copyright terms: Public domain W3C validator