ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  simpl2l Unicode version

Theorem simpl2l 1019
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpl2l  |-  ( ( ( ch  /\  ( ph  /\  ps )  /\  th )  /\  ta )  ->  ph )

Proof of Theorem simpl2l
StepHypRef Expression
1 simp2l 992 . 2  |-  ( ( ch  /\  ( ph  /\ 
ps )  /\  th )  ->  ph )
21adantr 274 1  |-  ( ( ( ch  /\  ( ph  /\  ps )  /\  th )  /\  ta )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    /\ w3a 947
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-3an 949
This theorem is referenced by:  xaddass  9620  xrbdtri  11013
  Copyright terms: Public domain W3C validator