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

Theorem keephyp3v 3787
 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 3737 . . . . . 6
32eqcomd 2440 . . . . 5
4 keephyp3v.1 . . . . 5
53, 4syl 16 . . . 4
6 iftrue 3737 . . . . . 6
76eqcomd 2440 . . . . 5
8 keephyp3v.2 . . . . 5
97, 8syl 16 . . . 4
10 iftrue 3737 . . . . . 6
1110eqcomd 2440 . . . . 5
12 keephyp3v.3 . . . . 5
1311, 12syl 16 . . . 4
145, 9, 133bitrd 271 . . 3
151, 14mpbii 203 . 2
16 keephyp3v.8 . . 3
17 iffalse 3738 . . . . . 6
1817eqcomd 2440 . . . . 5
19 keephyp3v.4 . . . . 5
2018, 19syl 16 . . . 4
21 iffalse 3738 . . . . . 6
2221eqcomd 2440 . . . . 5
23 keephyp3v.5 . . . . 5
2422, 23syl 16 . . . 4
25 iffalse 3738 . . . . . 6
2625eqcomd 2440 . . . . 5
27 keephyp3v.6 . . . . 5
2826, 27syl 16 . . . 4
2920, 24, 283bitrd 271 . . 3
3016, 29mpbii 203 . 2
3115, 30pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wceq 1652  cif 3731 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-if 3732
 Copyright terms: Public domain W3C validator