MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp2i Unicode version

Theorem simp2i 965
Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)
Hypothesis
Ref Expression
3simp1i.1  |-  ( ph  /\ 
ps  /\  ch )
Assertion
Ref Expression
simp2i  |-  ps

Proof of Theorem simp2i
StepHypRef Expression
1 3simp1i.1 . 2  |-  ( ph  /\ 
ps  /\  ch )
2 simp2 956 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ps )
31, 2ax-mp 8 1  |-  ps
Colors of variables: wff set class
Syntax hints:    /\ w3a 934
This theorem is referenced by:  hartogslem2  7274  harwdom  7320  divalglem6  12613  strleun  13254  birthdaylem3  20264  birthday  20265  divsqrsum  20292  harmonicbnd  20313  lgslem4  20554  lgscllem  20558  lgsdir2lem2  20579  mulog2sum  20702  vmalogdivsum2  20703  siilem2  21446  h2hva  21570  h2hsm  21571  hhssabloi  21855  elunop2  22609  rrisgrp  25441  wallispilem3  27919  wallispilem4  27920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
  Copyright terms: Public domain W3C validator