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

Theorem adantlrl 473
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.)
Hypothesis
Ref Expression
adantl2.1  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
Assertion
Ref Expression
adantlrl  |-  ( ( ( ph  /\  ( ta  /\  ps ) )  /\  ch )  ->  th )

Proof of Theorem adantlrl
StepHypRef Expression
1 simpr 109 . 2  |-  ( ( ta  /\  ps )  ->  ps )
2 adantl2.1 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
31, 2sylanl2 400 1  |-  ( ( ( ph  /\  ( ta  /\  ps ) )  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
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 is referenced by:  mapxpen  6710  recexgt0sr  7549  fsumabs  11202  fsumiun  11214
  Copyright terms: Public domain W3C validator