ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp1i Unicode version

Theorem simp1i 990
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
simp1i  |-  ph

Proof of Theorem simp1i
StepHypRef Expression
1 3simp1i.1 . 2  |-  ( ph  /\ 
ps  /\  ch )
2 simp1 981 . 2  |-  ( (
ph  /\  ps  /\  ch )  ->  ph )
31, 2ax-mp 5 1  |-  ph
Colors of variables: wff set class
Syntax hints:    /\ w3a 962
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105
This theorem depends on definitions:  df-bi 116  df-3an 964
This theorem is referenced by:  find  4513  structfn  11987  strleun  12057
  Copyright terms: Public domain W3C validator