ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simp-4r Unicode version

Theorem simp-4r 510
Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)
Assertion
Ref Expression
simp-4r  |-  ( ( ( ( ( ph  /\ 
ps )  /\  ch )  /\  th )  /\  ta )  ->  ps )

Proof of Theorem simp-4r
StepHypRef Expression
1 simpllr 502 . 2  |-  ( ( ( ( ph  /\  ps )  /\  ch )  /\  th )  ->  ps )
21adantr 271 1  |-  ( ( ( ( ( ph  /\ 
ps )  /\  ch )  /\  th )  /\  ta )  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  simp-5r  512  fimax2gtri  6671  finexdc  6672  exmidfodomrlemr  6882  exmidfodomrlemrALT  6883  supinfneg  9137  infsupneg  9138  hashunlem  10266  sumeq2  10802  fsumconst  10902
  Copyright terms: Public domain W3C validator